Physics XI-Short Questions

ALI RAZA (STUDENT AT FAUJI FOUNDATION H.S.S INTER COLLEGE TALAGANG, CHAKWAL

PHYSICS-XI

CHAPTER 1: MEASUREMENTS

1.1. Name several repetitive phenomenon occurring in nature, which could serve as reasonable time standard.

Any natural phenomenon that repeats itself after exactly same time interval can be used as a measure of time. The measurement is based upon the counting on repetitions. Following are some of the repetitive phenomenon occurring in nature, which could serve as reasonable time standards: (i) Rotation of earth around the sun (ii) Rotation of moon around the earth (iii) Change of shadow of an object in the sun during daytime (iv) Movement of stars during nighttime (v) Oscillating pendulums by finding their frequencies (vi) Rotation of planets in a solar system (vii) The dropping of certain mass of water or pouring of certain mass of sand through a hole (viii) Characteristic vibrations of crystals such as quartz crystal

1.2. Give the draw backs to use the period of a pendulum as a time standard.

As according to following formula

The time period of simple pendulum depends on the length and value of g at any place. The period of pendulum may not be used as time standard because of following reasons; (i) The value of g is different at different places i.e. it is low in Murree as compared to Karachi. It

is because;

(ii) The summer season can also effect the time period of pendulum due to temperature variations because

(iii) Surrounding atmosphere or air resistance may affect the time period of the simple

pendulum.

1.3. Why do we find it useful to have two units for the amount of substance, the kilogram and the mole?

We find it useful to have two units for the amount of mass because; Kilogram It is useful when we want to consider a specific amount of mass without considering the number of microscopic atoms or molecules present in it i.e. it is a unit used at macroscopic level. Its symbol is kg. For example: All masses in a physics or engineering laboratories Mole It is useful when we want to consider fixed number of atoms or molecules of a system i.e. it is a unit used at microscopic level. Mole represents a fixed number of molecules or atoms of any substance. These are 6.022 x 1023 atom or molecules in one mole. Its symbol is mol. For example: 1 g of hydrogen = 1 mole

1 g of water (H20) = 1 mole

1.4. Three students measured the length of a needle with a scale on which minimum division is 1mm and recorded as (i) 0.2145 m (ii) 0.21 m (iii) 0.214 m which record is correct and why?

The record (iii) 0.214 m is correct. It is because least count of a scale is 1 mm, which is equal to 1/1000 m or 0.001 m. As length can be measured more accurate up to three decimal places therefore other two records are not as much accurate as third one.


1.5. An old saying is that “A chain is only as strong as its weakest link”. What analogous statement can you make regarding experimental data used in a computation?

The analogous statement regarding experimental data used in computation is as follow; “A result obtained by mathematical computation of experimental data is only as much accurate as its least accurate reading in the experimental data.”

1.6. The period of simple pendulum is measured by a stopwatch. What types of errors are possible in the time period?

When the time period of simple pendulum is measured by a stopwatch then following types of errors are possible: (i) Systematic Errors

The error is due to the fault in the measuring instruments like stopwatch or vernier calipers. It can occur due to zero error in the stopwatch or poor calibration of stopwatch. This error can be removed by applying zero correction.

(ii) Personal Errors This error takes place due to the faulty procedure of observer or negligence and inexperience of a person. Error in timing occurs when the stopwatch is started and when it is stopped.

1.7. Does a dimensional analysis give any information on constant of proportionality that may appear in an algebraic expression? Explain.

No, dimensional analysis does not give any information about the constant of proportionality or dimensionless constant k. this constant k can be determined experimentally or theoretically. Dimensional analysis provides us information only about following: (i) Checking the homogeneity of physical equation (ii) Deriving a possible formula For Example (i) The relation for time period of simple pendulum is

(ii) Similarly in Stokes law

Here in above two equations of constant is determined theoretically or experimentally.

1.8. Write the dimensions of (i) Pressure, (ii) Density

(i) Pressure As we know

By applying dimensional analysis

As [F] = [MLT-2] and [A] = [L2] [P] = [MLT-2] / [L2]

Hence [P] = [ML-1T-2]

(ii) Density As we know

By applying dimensional analysis

As [m] = [M] and [V] = [L3] [ρ] = [M] / [L3]

Hence [ρ] = [ML-3]

1.9. The wavelength λ of a wave depends on the speed v of the wave and its frequency f. Knowing that [λ] = [L], [v] = [L T-1] and [f] = [T]-1

Decide which of the following is correct, f = v λ or f = v / λ

For f = v λ By applying dimensional analysis

As [f] = [T-1] , [v] = [LT-1] and [λ] = [L]

[T-1] = [LT-1][L] [T-1] = [L2T-1]

Both of the sides are not equal so this equation is not dimensionally correct.

For f = v / λ By applying dimensional analysis

As [f] = [T-1] , [v] = [LT-1] and [λ] = [L]

[T-1] = [LT-1]/[L] [T-1] = [T-1]

Both of the sides are equal so this equation is dimensionally correct.


Decision: The correct equation from, the given ones is

CHAPTER 2: SCALARS AND VECTORS

2.1. Define the terms (i) Unit vector, (ii) Position vector and (iii) Components of a vector.

(i) Unit Vector Definition: A unit vector in a given direction is a vector with magnitude one in that direction. It is used to represent the direction of a vector. Representation: A unit vector in the direction of A is written as Â, which we read it as “A hat”. Formula: As we know for vector A,

If we want to find the unit vector Â, it is obtained by dividing the vector with its magnitude as,

Three Dimensional Axes:

The directions along x, y, and z axes are generally represented by unit vectors , , and , respectively (Fig. a).

(a) (b) (c)

Other unit vectors: Unit vectors may be defined for any direction. Two of the most frequently used unit vectors are the vector , which represents the direction of the vector r (Fig. b) and the vector which represents the direction of a normal drawn on a specified surface (Fig. c)

(ii) Position Vector Definition: The position vector is a vector that describes the location of a point with respect to the origin. Representation: It is represented by a straight line drawn in such a way that its tail coincides with the origin and the head with point in the plane or space as shown in the figure. Formula: The position of vector r of point P (a,b) in xy plane is given by

The magnitude of vector r is given as

Similarly the position of vector r of point P (a,b,c) in space plane is given by

The magnitude of vector r is given as


(iii) Components of a Vector Definition: A component of a vector is its effective value in a given direction. A vector may be considered as the resultant of its components along the specified directions. It is usually convenient to resolve a vector into components along mutually perpendicular directions. Such components are called rectangular components.

Derivation of rectangular components: Let there be a vector A represented by OP making angle θ with the x-axis. Draw projection OM of vector on x-axis and projection ON of vector OP on y-axis as shown. Projection OM being along x-direction is represented by Axi and projection ON = MP along y-direction represented by Ayj. By head to tail rule;

Axi + Ayj Thus, Axi and Ayj are the components of vector A, since these are right angle to each other, hence they are called rectangular components of A. Considering the right angle OMP, the magnitude of Axi is given as perpendicular As,

Hence, Ax = A cos θ

And that of Ayj is given as, As,

Hence, Ay = A sin θ

Determination of vector from rectangular components: If the rectangular components of a vector, as shown in figure are given, we can find out the magnitude of vector by using Pythagorean theorem. In the right angled ∆ OMP,

And the direction θ is given by As,

or

2.2. The vector sum of three vectors gives a zero resultant. What can be the orientation of the vectors?

If three vectors such that they can be represented by the three sides of a triangle taken in cyclic order then the vector sum or resultant of the three vectors is zero. Explanation: Consider three vectors, A, B and C as shown in the figure. It is clear that sum of

the vectors is zero because tail of the first vector coincides with the head of

the last vector. Here


2.3. Vector A lies in the xy plane. For what orientation will both of its rectangular components be negative? For what orientation will its components have opposite signs?

Vector A lies in an xy plane. Case-I: The orientation of both of its components i.e. horizontal and vertical component is negative if they lie in III-Quadrant, as shown in the figure (a). Since, cos (180 + θ) = -cos θ sin (180 + θ) = -sin θ

(a) (b) (c) Case-II: The orientation of both of its components i.e. horizontal and vertical component is opposite if they lie in II-Quadrant and IV-Quadrant, For second quadrant, horizontal component of vector A is negative and vertical component is positive as shown in figure (b). Whereas in fourth quadrant, horizontal component of vector A is positive and vertical component is negative as shown in figure (c).

2.4. If one of the components of a vector is not zero, can its magnitude be zero? Explain.

No, its magnitude can never be zero. Explanation: As the magnitude of vector A is given by

If one component let say Ay = 0 then

------------------------------(i)

If Ax = 0 then

------------------------------(ii)

Above of two equations show that magnitude of the vector will be zero only when all of its

components are zero.

2.5. Can a vector have a component greater than the vector’s magnitude?

The rectangular components of a vector can never be greater than the vector’s magnitude but it may equal to the vector’s magnitude because components is always a part of the resultant vector. That is why the magnitude of the component will be less than that of resultant vector. Explanation: As the magnitude of vector A is given by

or

Here there are four possible conditions; (i) A2 ≥ Ax2

(ii) A2 ≥ Ay2

(iii) A ≥ Ax2


(iv) A ≥ Ay2

Of course, if the two vectors of the same magnitude act as an angle of 120° with each other, then

Here, Magnitude of C = Magnitude of A = Magnitude of B Hence, the maximum value of magnitude of a component can be equal to the magnitude of the resultant vector.

2.6. Can the magnitude of a vector have a negative value?

No, the magnitude of a vector cannot be negative. Explanation: As the magnitude of vector A is given by

As the squares of real quantities always, give positive value. Let Ax = -8 and Ay = 5 then

Secondly, sometimes the vector is represented by -5A or -7A. Hence, 5 or 7 is the magnitude of the vector while negative sign indicates the direction of a vector. Therefore, the magnitude of vector cannot have negative value.

2.7. If A + B = 0, What can you say about the components of the two vectors?

If A + B = 0, then it can be written as,

These vectors can be expressed in terms of rectangular components as

also

By comparing the coefficients of unit vectors i and j, we get, Ax = -Bx ----------------------- (I) Ay = -By ----------------------- (II) From (I) and (II) we can write, Ax + Bx = 0 Ay + By = 0 Hence it is concluded that if A + B = 0, then the sum of the magnitudes of their respective components will also be zero.

2.8. Under what circumstances would a vector have components that are equal in magnitude?

It is possible only when the vector makes an angle of 45° with x-axis. Proof: Let Ax and Ay be the magnitude of rectangular components of vector A, We have to prove that Ax = Ay

So,

Then

Therefore a vector would only have components equal in magnitude when = 45°


2.9. Is it possible to add a vector quantity to a scalar quantity? Explain.

No, it is not possible to add a vector to a scalar quantity. Explanation: Only physical quantities of same nature can be added. Both physical quantities are different in their physical nature. (i) Scalars consist of only magnitudes with no direction and they can be added by simple

arithmetical rules. (ii) Vectors are composed of both magnitudes and directions and they can be added by special

rules (vector algebra). Hence, it is not possible to add a scalar to vector or a vector to scalar quantity. Example: Let if we want to add 5 meters of distance into 10 cm of displacement (north) it is impossible.

2.10. Can you add zero to a null vector?

No, it is not possible to add a zero to a null vector. Explanation: As null vector have magnitude zero and arbitrary direction whereas zero is a scalar only having a magnitude. However, if zero vector is added to null vector then we get same null vector as result, i.e.

. Only physical quantities of same nature can be added. Both physical quantities are different in their physical nature. (i) Scalars consist of only magnitudes with no direction and they can be added by simple

arithmetical rules. (ii) Vectors are composed of both magnitudes and directions and they can be added by special

rules (vector algebra). Hence, it is not possible to add a scalar to vector or a vector to scalar quantity.

2.11. Two vectors have unequal magnitudes. Can their sum be zero? Explain.

No, two vectors having unequal magnitudes cannot be combined to give zero as resultant, whatever their orientation may be. Explanation: The sum of two vectors can be zero if both are equal and opposite in direction. Let A and B are two vectors having same magnitude and direction then their sum will be zero because,

Hence, it is completely impossible to have zero as resultant vector by combing two vectors having unequal magnitudes.

2.12. Show that the sum and difference of two perpendicular vectors of equal lengths are also perpendicular and of the same length.

Consider two vectors and as shown in figure. Given:

(i) Length of vectors and is equal i.e. A = B

(ii) Angle between vectors and is 90° To prove:

(i)

(ii) Considerations: By using head to tail rule,

And


Proof:

(i) Magnitude of

(ii) Magnitude of

From (i) and (ii) it is clear that

----------------------------------------------------(i) proved Since A = B

LOM = NOM = 45°

Therefore, the angle between Here,

LON = LOM + NOM = 45° + 45° = 90° So, it is proved that,

----------------------------------------------------(ii) proved

2.13. How would the two vectors of the same magnitude have to be oriented, if they were to be combined to give a resultant equal to a vector of the same magnitude?

Given: Let A1 and A2 are two vectors having same magnitude equal to say A. i.e. A1 = A2 = A. Magnitude of Resultant R = A To find: Orientation of vector A1 and A2

Calculations: As,

A1 = A2 = R = A So,

By squaring both sides, we get

or

Hence, the orientation between two vectors will be 120°.


2.14. The two vectors to be combined have magnitudes 60 N and 35 N. Pick the correct answer from those given and tell why is it the only one of the three that is correct. (i) 100 N (ii) 70 N (iii) 20 N

The correct answer is 70 N. Explanation: (i) Sum of two vectors is maximum, if they are parallel to each other. Here,

Vector 1 + Vector 2 = 60 N + 35 N = 95 N (ii) Sum of two vectors is minimum, if they are opposite to each other. Here,

Vector 1 + Vector 2 = 60 N + (-35 N) = 25 N It shows that the sum is equal to or greater than 25 N and equal or less than 95 N. hence the possible answer is 70 N.

2.15. Suppose the sides of a closed polygon represent vector-arranged head to tail. What is the sum of these vectors?

The sum of these vectors will be zero. Reason: As we know that, the resultant of a number of vectors, which makes the closed path as in polygon, is

equal to zero. If the vectors are represented by the sides of a closed polygon, then they are added by using head to tail rule.

Thus, the sum will be zero because the tail of the first vector coincides with the head of last vector. Hence,

Therefore, the sum of the vectors of closed polygon becomes zero, because their resultant is represented in magnitude and direction by the closing side of the polygon taken in opposite order.

2.16. Identify the correct answer; (i) Two ships X and Y are travelling in different directions at equal speeds. The actual direction of

motion of X is due north but to an observer on Y, the apparent direction of motion of X is northeast. The actual direction of motion of Y as observed from the shore will be: (A) East (B) West (C) South-East (D) South-West

(ii) A horizontal force F is applied to a small object P of mass M at rest on a smooth plane inclined at an angle θ to the horizontal as shown in the figure. The magnitude of the resultant force acting up and along the surface of the plane, on the object is: (a) F cos θ - mg sin θ (b) F sin θ - mg cos θ (c) F cos θ + mg cos θ (d) F sin θ + mg sin θ (e) mg tan θ

(i) The correct answer is (B) West. Reason: Let vx = velocity of ship X vy = velocity of ship Y vx - vy = Velocity of ship X relative to ship Y

or

This shows that vy is directed opposite i.e. west.

θ

P F


(ii) The correct answer is (A) F cos θ - mg sin θ. Reason:

Here by resolving F and W into rectangular components along and perpendicular the inclined plane, we have F cos θ - mg sin θ = net force acting up along the plane.

2.17. If all the components of the vectors, A1 and A2 were reversed, how would this alter A1 x A2 ?

There would be no change in if we reverse the direction of both vectors. Reason: If all the components of the vectors A1 and A2 are reversed, then both these vectors will be written as -A1 and -A2 respectively. Therefore, Therefore,

(a) Actual (b) Reversed

Hence, the vector product of two vectors will remain unchanged even by reversing all the components of vectors.

2.18. Name the three different conditions that could make A1 x A2 = 0.

If are two vectors then

Conditions: Proof:

is zero if , (i) is a null vector i.e. .

(ii) are parallel i.e. .

(iii) are anti-parallel i.e. .

2.19. Identify true or false statements and explain the reason. (a) A body in equilibrium implies that it is not moving nor rotating. (b) If coplanar forces acting on a body form a closed polygon, then the body is said to be in equilibrium.

(a) It is false because in dynamic equilibrium body may move or rotate with uniform velocity.

(b) It is false because in this case, first condition of equilibrium i.e. is satisfied and the body is

said to be in translational equilibrium.


2.20. A picture is suspended from a wall by two strings. Show by diagram the configuration of the strings for which the tension in the strings will be minimum.

Let the picture is suspended from the wall by two strings (fig. a).

(fig. a)

Resolving the tension into its rectangular components, gives that

From this relation the tension will be minimum if sin is 1 i.e.

sin

Then,

As

Thus, we concluded that the tension is maximum if strings are vertical (fig. b).

(fig. b)

2.21. Can a body rotate about its centre of gravity under the action of its weight?

No, a body cannot rotate about its center of gravity under the action of its weight. Reason: As we know the centre of gravity is a point where the whole weight of the body acts. It means that the weight passes through the axis of rotation. Therefore, the moment arm becomes zero. As, l = 0, then

Hence, the torque will also be zero. We concluded that, a body could not rotate about its center of gravity under the action of its weight.


CHAPTER 3: FORCE AND MOTION

3.1. What is the difference between uniform and variable velocity. From the explanation of variable velocity, define acceleration. Give SI units of velocity and acceleration.

Difference between Uniform and Variable Velocity:

Uniform Velocity Variable Velocity

Definition: When body covers equal displacement in equal intervals of time, however small the interval may be, then velocity is called uniform velocity.

Definition: When body covers unequal displacement in equal intervals of time, however small the interval may be, then velocity is called variable velocity.

Magnitude: It remains same with direction.

Magnitude: It may or may not change with direction.

Direction: When body moves with uniform velocity its direction of motion does not change.

Direction: When body moves with variable velocity its direction of motion changes.

Example: A body moving on a straight path with constant speed will have uniform velocity.

Example: A body moving on a curved path with changing speed will have variable velocity.

Figure: Figure:

Definition of Acceleration: “When initial velocity ‘vi’ of a body changes velocity ‘vf’. Then change in velocity ‘vf-vi’ with time ‘t’ produces acceleration ‘a’ in the body.” OR “The time rate of change of a velocity of a body is called acceleration.” Mathematically,

SI units of Velocity and Acceleration: SI unit of velocity is meter per second (ms-1). SI unit of acceleration is meter per second square (ms-2).

3.2. An object is thrown vertically upward. Discuss the sign of acceleration due to gravity, relative to velocity, while the object is in air.

The sign of acceleration due to gravity relative to velocity is negative. Reason: All those quantities are assigned to be negative sign whose direction is opposite to the direction of the initial velocity. Therefore, when the object is thrown upward, the direction of gravitational pull is opposite to the direction of initial velocity so the sign of acceleration due to gravity relative to velocity is negative. However, if the object is moving downwards then the sign of acceleration relative to velocity will be taken as positive because velocity of the object and acceleration ‘g’ are in the same direction.

Earth

m

Moving with

velocity v

g acting

downward


3.3. Can the velocity of an object reverse direction when acceleration is constant? If so, give an example.

Yes, it can be possible that the velocity of an object reverse direction when acceleration is constant. Reason: When s body is thrown vertically upward, its velocity goes on decreasing due to gravity acting

downward. When the body reaches the maximum height, its velocity becomes zero, and then the body

reverses its direction and starts moving back vertically downward. During the whole process of motion, the magnitude of the acceleration due to gravity remains

constant i.e. 9.8 ms-2.

3.4. Specify the correct statement: (a) An object can have a constant velocity even its speed is changing. (b) An object can have a constant speed even its velocity is changing. (c) An object can have a zero velocity even its acceleration is not zero (d) An object subjected to a constant acceleration can reverse its velocity.

Statement (b), (c) and (d) are correct. Reason: (a) (FALSE) Velocity remains constant when both speed and direction does not change. As speed is

changing, so velocity will not be constant. (b) (TRUE) When an object moves in a circle, it has changing velocity because its moves with

constant speed but the direction continuously changes.

(c) (TRUE) When pendulum is displaced from its mean position O, it performs to and fro motion. At

extreme position, velocity is zero but acceleration is not zero but has a maximum value.

OR When a moving object is stopped by applying sudden hard brakes, velocity becomes zero at that instant but acceleration is not.

(d) (TRUE) When an object is thrown vertically up, after reaching maximum height, its velocity reverses but its acceleration remains constant i.e. 9.8 ms-2.

Earth

m

Moving with

velocity v

g acting

downward

v = 0 a = max.

v = 0 a = max.

v = max. a = 0


3.5. A man standing on the top of a tower throws a ball straight up with initial velocity vi and at the same time throws a second ball straight downward with the same speed. Which ball will have larger speed when it strikes the ground? Ignore air friction.

Both the balls will hit ground with same speed. Reason:

The ball A which is thrown vertically up with the velocity vi will have same velocity vi when it reaches back to the top of the tower. Hence, this ball hit the ground with same speed.

When the second ball B is thrown vertically downward with initial velocity vi, it will also strike the ground with same speed. It results that both the balls hit the ground with the same speed i.e. vf = vi.

However, difference is that both the balls will hit the ground at different times due to different heights.

3.6. Explain the circumstances in which the velocity v and acceleration a of a car are (i) Parallel (ii) Anti-parallel (iii) Perpendicular to one another (iv) v is zero but a is not (v) a is zero but v is not zero

(i) When the velocity of the car is increasing along the straight path then velocity and acceleration are parallel to each other.

(ii) When the velocity of the car is decreasing along the straight path then velocity and acceleration are anti-parallel i.e. when the brakes are applied to a moving car.

(iii) It the car is moving in a circular path then the velocity and acceleration are mutually perpendicular.

(iv) When the brakes are applied on a moving car, it slows down and comes to rest due to negative acceleration in the opposite direction. Thus, velocity is zero but acceleration is not zero. Here,

= = 0

Then acceleration is given as,

(v) When a car is moving with uniform velocity along a straight path, then acceleration is zero but velocity is not zero. Here,

= =


T

O

W

E

R

A

B vi

vi

vi = vf


3.7. Motion with constant velocity is a special case of motion with constant acceleration. Is this statement true? Discuss.

Yes, it is a true statement. Reason: When a body moves with uniform velocity, its acceleration is zero because in this case, the velocity changes at the same rate throughout the motion. Hence, the acceleration of the body will always remain constant during its motion that is equal to zero. As zero is also a constant quantity therefore, this is a special case of motion. Here,

= =


3.8. Find the change in momentum for an object subjected to a given force for a given time and state law of motion in terms of momentum.

Statement: Rate of change of momentum of a body is equal to the applied force and the change in momentum takes place in the direction of applied force. Proof:

Consider a body of mass ‘m’ moving with initial velocity ‘ ’. Let us suppose that an external force ‘ ’ acts upon it for time ‘t’ after which its velocity becomes ‘ ’. If this force produces an acceleration ‘ ’, then it is expressed as,

According to the Newton’s second law,

Putting (i)

This is Newton Second Law in terms of momentum. Here the unit of momentum given by the relation is newton second (N s).

3.9. Define impulse and show that how it is related to linear momentum.

Definition: “It is defined as the product of force and time.”

OR “When a large force acts on a moving body for short interval of time then the product of force and time is called impulse.” Mathematical form: Mathematically, it can be expressed as,

Relation: According to Newton Second law of motion, the force is defined as the rate of change of momentum. As,

Hence, impulse is equal to change of linear momentum.


Elastic Collision

Before After

Inelastic Collision

Before After

K.E. lost as Heat

or Sound

3.10. State the law of conservation of linear momentum, pointing out the importance of isolated system. Explain, why under certain conditions, the law is useful even though the system is not completely isolated?

Statement: It states that the total linear momentum of an isolated system always remains constant. Isolated System: A system, which is not acted upon by external forces, is called an isolated system. In this system, the bodies may interact with another and can exert force on another but no agency can exert a force on them. Importance of Isolated System: Its importance can be understood by many examples of isolated system which conserve momentum. (i) Molecules of a gas enclosed in a vessel at constant temperature (ii) Elementary particles of an atom, such as proton, electron and neutron

when they suffer collision (iii) Rocket and its fuel (iv) Gun and bullet (i.e. firing of bullet from gun) Application of not completely isolated system: In everyday life, when the effect of external forces (i.e. frictional and gravitational forces) is negligibly small as compared to the forces between the interacting objects, then this law becomes applicable. If the sum of all the forces acting the system is zero, between then this law is applicable.

3.11. Explain the difference between elastic and inelastic collisions. Explain how would a bouncing ball behave in each case? Give plausible reasons for the fact that K.E. is not conserved in most cases?

Difference between elastic and inelastic collision:

Elastic Collision Inelastic Collision

Definition: A collision in which both linear momentum and kinetic energy are conserved before and after the collision is called elastic collision.

Definition: A collision during which total momentum is conserved but total kinetic energy before and after collision is not conserved is called inelastic collision.

Case: It is an ideal case.

Case: It is a non-ideal case.

Direction: When body moves with uniform velocity its direction of motion does not change.

Direction: When body moves with variable velocity its direction of motion changes.

Example: Bouncing back of two hard balls from marble

floor Collision of gas molecules Collision of two smooth snooker/rubber balls

Example: Bouncing back of two hard balls from sandy

floor Collision of two tennis balls

Behaviour of bouncing ball: When the bouncing ball is dropped on hard marble floor, If ball rebounds to the same height from where it was

dropped then collision will be considered elastic because in this case little amount of K.E. is lost.

If ball does not rebound to original height then collision will be considered inelastic because in this case more K.E. is lost and used in producing sound, heat and to overcome friction.


K.E. is not conserved in most of cases: In actual practice every collision is inelastic in our daily life it is because K.E. before and after collision is not same. Following examples explain that K.E. is not conserved in most of cases. (i) When ball is dropped on sandy ground, it does rebounds to same height from where it was

dropped but it loses all of its K.E. In this case, K.E. before and after collision is not same.

(ii) When collision of truck with car takes place then original K.E. of car and truck is lost in

producing deformation and sound.

(iii) When bullet strikes with wall inelastic collision takes place.

3.12. Explain what is meant by projectile motion. Derive expressions for (a) the time of flight (b) the range of projectile. Show that the range of projectile is maximum when projectile is thrown at an angle of 45° with the horizontal.

Projectile Motion Definition: Projectile motion is two-dimensional motion under constant acceleration due to gravity. It is combination of two motions i.e. horizontal motion with constant velocity (∆v = 0) and vertical motion with constant acceleration (g = 9.8 ms-2). Projectile: It is an object performing projectile motion or projected in space with a certain vi in an arbitrary motion and then allowed to move under the influence of gravity. Trajectory: The path followed by the projectile during projectile motion is called trajectory. Examples: Football kicked off by a player Ball thrown by cricketer Missile fired from a launching pad Bullet fired from gun Batted baseball

Important equations: Horizontal motion

Inelastic Collision

Before After

K.E. lost as

heat or sound

K.E. K.E.

K.E. lost as heat or sound and

deformation energy


Y vi

θ X

Projection Landing Point Point

Y vi

θ X


R

The motion along x-axis remain constant i.e. ∆v = 0. It is because if we neglect air friction then there is no force acting on body. Then according to Newton’s First Law of Motion acceleration along x-axis remain constant because only force of gravity is acting on body so, ax = 0.

Horizontal distance

Horizontal velocity

Vertical motion In absence of air resistance, the only force acting on the body is force of gravity. A body accelerates downward with vertical acceleration i.e. ay = g.

Vertical distance As, vi = 0 so

Vertical velocity

Magnitude of velocity

Direction of velocity

Expressions Time of the flight: Definition

The time taken by a body to cover the distance from the place of its projection to the place where it hits the ground at the same level is called the time of the flight.

Derivation By considering second equation of motion;

Here S = h = 0 because body goes up and come to same level vi = vi sin θ because body is moving vertically i.e. along y-axis a = -g because body is freely falling and moving upward against the direction of gravity. T = time of the flight Hence,

By taking ‘t’ common

Range of the projectile: Definition

Maximum distance which projectile covers in the horizontal direction is called the range of the projectile.

Derivation Using formula of horizontal distance

Here x = R = Range of the projectile vx = vix = vi cos θ


Y viy = 0 vix

θ X

Hence,

As we know according to formula in trigonometric ratios,

then

Maximum Range: As we have given θ = 45° then from (ii) (As sin 90° = 1)

Hence it in proved that if θ = 45° then range of projectile will be maximum.

3.13. At what point or points in its path does a projectile have its minimum speed, its maximum speed?

Minimum Speed: The speed of projectile is minimum at the maximum height because at this height vertical component of velocity becomes zero.

Proof As,

At maximum height, vi becomes zero so

Therefore, projectile has minimum speed at maximum height Maximum Speed: The speed of projectile is maximum at the point of projection and also just before it strikes the ground (level of projection/landing) because the vertical component of velocity is maximum at

these points. Proof As,

θ = 90°

Therefore, projectile has maximum speed at point of projection and landing.

3.14. Each of the following questions is followed by four answers, one of which is correct answer. Identify that answer. (i) What is meant by a ballistic trajectory?

a. The paths followed by an un-powered and unguided projectile. b. The path followed by the powered and unguided projectile. c. The path followed by un-powered and guided projectile. d. The path followed by powered and guided projectile.

(ii) What happens when a system of two bodies undergoes an elastic collision? a. The momentum of the system changes. b. The momentum of the system does not change. c. The bodies come to rest after collision. d. The energy conservation law is violated.

Y vi

viy

X vix viy vi

vix



3F

2F

1F

0 1L 2L 3L

(i) The statement (a) is correct. It is because the path followed by an unpowered and unguided projectile is called ballistic trajectory.

(ii) The statement (b) is correct. It is because according to law of conservation of momentum, the momentum of the isolated system such as in elastic collision does not change i.e. remain same.

CHAPTER 4: WORK AND ENERGY

4.1. A person hold a bag of groceries while standing still, talking to a friend. A car is stationary with its engine running. From the standpoint of work, how are these two situations similar?

In both the cases, the work done is zero. Reason: As the person and the car, both are at rest. So in both the cases the displacement is zero i.e. d = 0. According to the definition of the work,

Thus in both the situations the work done is zero. Therefore, from the standpoint of work, these two situations are similar.

4.2. Calculate the work done in kilo joules in lifting a mass of 10 kg (at a steady velocity) through a vertical height of 10 m.

Given Data: Mass = m = 10 kg Height = h = 10 m To Find: Work = W = ? (kJ) Formula Used:

Calculations: As the work done is in the form of P.E. so,

For conversion in kJ,

Result: By lifting a mass of 10 kg at steady velocity through a vertical height of 10 m the work done is equal to 980 J or 0.980 kJ.

4.3. A force F acts through a distance L. the force is then increased to 3 F, and then acts through a further distance of 2 L. Draw the work diagram to scale.

As area under the force displacement graph is equal to the work done by the body. So,

4.4. In which case is more work done? When a 50 kg bag of books is lifted through 50 cm, or when a 50 kg crate is pushed through 2 m across the floor with a force of 50 N?

Case 1


Given Data: Mass = m = 50 kg Height = h = 50 cm = 0.5 m To Find: Work1 = W1 = ? Formula Used:


----------------------------------- (I) Case 2 Given Data: Mass = m = 50 kg Displacement = d = 2 m To Find: Work2 = W2 = ? Formula Used:


----------------------------------- (II) Result From (I) and (II) it is proved that more work is done in case 1.

4.5. An object has 1 J of potential energy. Explain what it means?

An object having 1 J of potential energy means that the work done stored in the object in the form of potential energy has the capacity to do work of 1 J. For example: If an object is lifted up by the force of one newton through a height of one meter, the work done is stored in the object as potential energy of one joule. If the object is allowed to fall vertically downward, it has the capacity to do 1 J work.

4.6. A ball of mass m is held at a height h1 above a table. The tabletop is at a height h2 above the floor. One student says that the ball has potential energy mgh1 but another says that it is mg(h1 + h2). Who is correct?

Both of them are correct. Reason: Since P.E. is always with respect to some reference point. Therefore, we can say that first student has measure P.E. with

respect to tabletop (i.e. =mgh1). And the second student has measure P.E. with respect to floor

[i.e. =mg (h1 + h2)].

4.7. When a rocket re-enters the atmosphere, its nose cone becomes very hot. Where does this heat energy come from?

There are large number of dust particles and water vapours present in the air. When a rocket re-enters the atmosphere, it has to face the resistance due to particles. Some of its K.E. is converted to heat energy. Therefore, the nose cone of the rocket becomes very hot due to the heat energy produced by the fluid friction of atmosphere.

h=

h1+

h2 h1

h2

Heat emits


4.8. What sort of energy is in the following: (a) Compressed spring (b) Water in a high dam (c) A moving car

(a) Elastic Potential Energy

(b) Gravitational Potential Energy

(c) Kinetic Energy

4.9. A girl drops a cup from a certain height, which breaks into pieces. What energy changes are involved?

As a cup is thrown from certain height, It loses its gravitational potential energy and gain kinetic energy. When it strikes the ground then part of this energy is used to break the cup and rest of the

energy converts to sound energy, kinetic energy of moving pieces and heat energy dissipated against friction.

4.10. A boy uses a catapult to throw a stone, which accidentally smashes a green house window. List the possible energy changes.

As a boy throws a stone by using catapult, It loses its elastic potential energy and gain kinetic energy. When it strikes the window then part of this energy is used to break the window into pieces and

rest of the energy converts to sound energy, kinetic energy of moving pieces and heat energy and may be some of light energy.

Gravitational Potential Energy

Kinetic Energy

Sound Energy Heat EnergyKinetic Energy of

moving pieces

Elastic Potential

Energy

Kinetic Energy

Sound Energy

Heat Energy

Kinetic Energy of

moving pieces

Light Energy


CHAPTER 5: CIRCULAR MOTION

5.1. Explain the difference between tangential velocity and the angular velocity. If one of these is given for a wheel of known radius, how will you find the other?

Difference between Tangential and Angular Velocity:

Tangential Velocity Angular Velocity

Definition: The velocity, which is directed along the tangent at any point on the circle or curve path, is called tangential velocity.

Definition: Rate of change of angular displacement of an object moving along a circle is called angular velocity.

Unit of Measurement: It is denoted by or and measured in meter per second (ms-1) and sometimes in kilometer per hour (kmh-1)

Unit of Measurement: It is denoted by and measured in radians per second (rad s-1) and sometimes in revolutions per minute (rev m-1)

Formula:

Formula:

Direction: Its direction is along the tangent at any point on the circle or curve path.

Direction: Its direction is along the axis of rotation.

Figure:

Figure:

Determination: Linear velocity , angular velocity and radius r are related as,

When and r are known then tangential velocity can be determined by using above equation. When and r are known then can be determined by the relation,

5.2. Explain what is meant by centripetal force and why it must be furnished to an object if the object is to follow a circular path?

Definition: “When the body moves in a circle with constant speed, the force, which keeps the body in the circular path and always directed towards the centre of the circle is called centripetal force.” OR “The force needed to bend the normally straight path of the particle into a circular path is called centripetal force.” Mathematical form: Mathematically, it is given as,

Significance: It is perpendicular to the tangential velocity and directed towards the center of the circular path. Without centripetal force, body will move along a tangent. Centripetal force changes the direction of the body at every instant to move in its circular path and produces the acceleration. It is always needed to maintain the body in its circular path.


5.3. What is meant by moment of inertia? Explain the significance.

Definition: “The product of mass of particle and square of its perpendicular distance from the axis of rotation is called moment of inertia.” OR “The property of a body to resist any change in its state of rest or uniform angular velocity is called moment of inertia.” Mathematical form: Mathematically, it is given as,

Thus, moment of inertia depends on; Mass of body Distance of body from the axis of rotation

Moment of Inertia of Some Bodies:

Body Shape I Body Shape I

Point Mass

Solid Disc

or Cylinder

Thin Rod

Sphere

Thin Ring or Hoop

Significance: It plays same role during angular motion, which is played by mass during linear motion. Mass is measure of linear inertia while moment of inertia is a measure of rotational inertia of a body. (a) Mass determine the linear acceleration as for the body in linear motion, the acceleration is

directly proportional to the force acting upon the body,

(b) Moment of inertia determines the angular acceleration as for the body in angular motion, the acceleration is directly proportional to the torque acting upon the body

5.4. What is meant by angular momentum? Explain the law of conservation of angular momentum.

Angular Momentum: Definition:

A particle is said to possess an angular momentum about a reference axis if it so moves that its angular position changes relative to that reference axis. Formula:

The angular momentum of a particle of mass m moving with velocity and momentum relative to origin is defined as

Where, is the position vector of the particle at that instant relative to the origin.

Quantity:

It is a vector quantity.


Magnitude: Its magnitude is given by,

Here, θ is the angle between Direction:

The direction of is perpendicular to the plane formed by and its sense is given by the right hand rule of vector product. Unit and Dimensions:

Its unit is kgm2s-1 or J s. the dimensions are [ML2T-1]. Second Definition:

The angular momentum is also defined as the product of moment of inertia I and angular velocity of the body. Formula:

Where is the position vector of the particle at that instant relative to the origin. Law of Conservation of Angular Momentum: Statement:

The law of conservation of momentum states that if no external torque acts on a system, the total momentum of the system remains constant. Mathematical form:

Explanation:

Consider the example of a stone whirled at the end of the string. If we stop exerting force on the string and allow it to wind on the finger, the length of the string will go on decreasing while the angular speed of the stone will go on increasing continuously. As no new torque acts on the stone (because force is zero), the angular momentum will remain constant. When the length of the string decreases, ‘I’ also decreases and for keeping constant, the angular speed increases. It can be expressed as,

If moment of inertia of body ‘I’ decreases, its angular velocity increases, so that their product remains constant.

5.5. Show that orbital angular momentum Lo = mvr.

Proof: Consider a body of mass m moving in a circle of radius r as shown in figure, As,

Its magnitude is given by,

Where θ is a angle between r and p, and p = mv So,

As the angle between r and v is 90°

sin 90° = 1, so

Hence, it is proved that orbital angular momentum Lo = mvr.

5.6. Describe what should be the minimum velocity, for a satellite, to orbit close to the Earth around it.

Critical Velocity: The minimum velocity needed to orbit a satellite close to the earth is called critical velocity. Calculation: When the satellite is moving in a circle, it has centripetal acceleration,


In a circular orbit around the earth, the centripetal acceleration is supplied by gravity can be found as,

But F = w = mg

Hence,

Where R is the radius of Earth i.e. 6400 km or 6400000 m and g = 9.8 ms-2. Then,

This is the minimum velocity necessary to put a satellite into orbit around the earth.

5.7. State the direction of the following vectors in simple situations; angular momentum and angular velocity.

Right Hand Rule: Grasp the axis of rotation in your right hand, curl the fingers along the direction of rotation then the thumb will represent the direction of angular quantity.

Direction of Angular Momentum:

As we know . Angular momentum is a vector quantity. Its direction is perpendicular to the plane formed by or it is directed along the axis of rotation. When the sense of rotation is clockwise, it is directed along axis of rotation in downward direction and when the sense of rotation is anticlockwise, then it is directed upward along the axis of rotation. Right hand rule help in this regard. Direction of Angular Velocity: As we know . Angular velocity is a vector quantity. Its direction is along the axis of rotation. When the sense of rotation is clockwise, it is directed along axis of rotation in downward direction and when the sense of rotation is anticlockwise, then it is directed upward along the axis of rotation. Right hand rule help in this regard.

5.8. Explain why an object, orbiting the Earth, is said to be freely falling. Use your explanation to point out why objects appear weightless under certain circumstances.

When the object is thrown horizontally fast enough from the certain height, so that the curvature of its match with the curvature of the Earth then the object simply revolve around the earth. Hence, the motion of object is under the constant acceleration due to gravity (equal to centripetal acceleration). Therefore, we can say the orbiting body is freely falling. Weightlessness of a body: A freely falling body moves under the action of gravitational force so that the object is said to be in state of weightlessness.

As a = g, so,


5.9. When mud flies off the tyre of a moving bicycle, in what direction does it fly? Explain.

The mud flies off due to tangential velocity. Reason: When the tyre rotates then centripetal force acts on the mud, which is equal to adhesive force between the tyre and mud. When the velocity of tyre is slow, then adhesive force, provide sufficient force and mud follow a circular path. As speed of the tyre increases, the adhesive force becomes weaker as compared to the cohesive forces between the particles of mud. Thus, adhesive force becomes unable to provide sufficient centripetal force. So, centripetal force becomes absent. As a result, mud flies off the tyre along the tangent to the rim of the tyre.

5.10. A disc and a hoop start moving down from the top of an inclined plane at the same time. Which one

will be moving faster on reaching the bottom?

Disc will move faster on reaching the ground. Proof: Speed of the hoop at the bottom of inclined plane is,

Speed of the disc at the bottom of inclined plane is,

or,

Physical Reason: The moment of Inertia of hoop is

The moment of Inertia of disc is

Angular velocity and moment of inertia are inversely proportional to each other. Since, the moment of inertia of disc is smaller than the moment of inertia of the hoop. Therefore, angular velocity of disc is greater than hoop.

5.11. Why does a diver change his body positions before diving in the pool?

The diver changes his body positions to spin himself faster, so that he may be able to take extra somersaults. Explanation: For this purpose, when the diver lifts off the diving board, his legs and

arms are fully extended in order to have a large moment of inertia about an axis. Thus, his angular velocity decreases. When

the moment of inertia increases, it means the value of increases in the formula

When he pulls his legs and arms into closed tuck position, his moment of inertia is reduced to a new value. Therefore, the value of his angular velocity increases. When decreases due to closed tuck position in this case

(mud flies off)


As the angular momentum is conserved, so

Hence the diver spins faster when moment of inertia becomes smaller and angular velocity increases to conserve angular momentum. In this way, he can make more somersaults.

5.12. A student holds two dumb-bells without stretched arms while sitting on a turntable. He is given a push until he is rotating at certain angular velocity. The student then pulls the dumbbell towards his chest. What will be the effect on rate of rotation?

The rate of rotation is greater when student pulls the dumb-bells towards his chest. Reason: According to law of conservation of momentum,

(a) When the student holds two dumb-bells by stretching his arms, then value of rotational inertia is

increased. Therefore, the rotational velocity is decreased.

(b) When the student pulls the dumb-bells towards his chest, the rotational inertia decreased. Therefore, the rotational velocity is increased.

(c) During this whole process, the total angular momentum remains constant.

5.13. Explain how much minimum number of geo-stationary satellites are required for global coverage of T.V. transmission.

Minimum three correctly positioned geo-stationary satellites are required for the global coverage of T.V. transmission. Reason: As each satellite in geo-stationary orbit may cover 120° of longitude so for whole populated surface of the earth, there must be minimum three correctly positioned geo-stationary satellites to provide the coverage of 360° of longitude.

120

°


CHAPTER 6: FLUID DYNAMICS

6.1. Explain what do you understand by the term viscosity?

Definition: An opposing force comes into play when one layer of fluid moves relative to another layer. This internal friction between two layers of fluid in relative motion is called viscosity or fluid friction. Representation: It’s coefficient is represented by a Greek letter “η” pronounced eta. Units: The units of a coefficient of viscosity are kgm-1s-1 or Nsm-2. Dimensions: The dimensions of viscosity are [ML-1T-1]. Examples: Substances that do not flow easily such as thick tar and honey etc; have large coefficient of

viscosity. Substances which flow easily, like water, have small coefficient of viscosity.

Some coefficients:

Material Viscosity at 30

°C (Nsm-2) Material Viscosity at 30

°C (Nsm-2) Material Viscosity at 30

°C (Nsm-2) Air 0.019 x 10-3 Benzene 0.564 x 10-3 Plasma 1.6 x 10-3

Acetone 0.295 x 10-3 Water 0.801 x 10-3 Glycerin 6.29 x 10-3 Methanol 0.510 x 10-3 Ethanol 1.000 x 10-3

6.2. What is meant by drag force? What are the factors upon which drag force acting upon a small sphere of radius r, moving down through liquid, depend?

Definition: An object moving through a fluid experiences a retarding force called drag force. It increase as the speed of the fluid increases. Stokes Law: The drag force F on a sphere of radius r moving slowly with speed v through a fluid of viscosity η is given by Stokes law as under,

Factors affecting: As according to the formula;

, it means as the coefficient of viscosity of an object increases the drag force also increases. depends on the material and shape of the object.

, it means as the radius of the spherical object increases the drag force also increases.

, it means as the speed of an object increases the drag force also increases. But at high speeds the force is no longer simply proportional to speed

6.3. Why fog droplets appear to be suspended in air?

Terminal velocity of a fog droplet is given as,

It shows, smaller the weight of sphere, smaller will be its terminal velocity Explanation: A fog droplet is a tiny drop having a very small weight. As the droplet falls, the drag force acting on it becomes equal to the weight of the droplet then net force acting on it is zero. Thus, the droplet will fall with terminal velocity (constant speed) whose value is very small. Therefore, the droplet drops so slowly that it appears to be suspended in air.

η F

v

r


6.4. Explain the difference between laminar flow and turbulent flow.

Laminar Flow Turbulent Flow

Definition: The flow is said to be streamline or laminar flow, if every particle that passes a particular point, moves along exactly the same path, as followed by particles, which passed, that points earlier.

Definition: The irregular or unsteady flow of the fluid is called turbulent flow.

Speed of Fluid: It occurs when speed of fluid is low called steady flow condition.

Speed of Fluid: It occurs when speed of fluid is fast

Streamlines: The direction of the streamlines is the same as the direction of the velocity of the fluid at that point.

Streamlines: The exact path of the particles cannot be predicted.

Example: Water flowing in stream have laminar flow.

Example: Water flowing in river have turbulent flow.

6.5. State Bernoulli’s relation to a liquid in motion and describe some of its applications.

In case of Extensive Question see textbook for convenience. Statement: When ideal fluid moves through uniform pipe, pressure P, kinetic energy K.E. and potential energy P.E. per unit volume remains constant at all points.

Assumptions: In deriving Bernoulli’s equation, we assume that,

Fluid is incompressible Fluid is non-viscous Flow is in steady state manner

Figure: Let us consider the flow of fluid through pipe in time t, Derivation: From BOOK, Page No 132-133 Applications:

The swing of cricket ball Lift produced in aeroplane wings Working of carburetor of car Blood flow Working of chimney Paint sprayers Working of filter pump Working of perfume sprayer

Explanation of Applications: Torricelli’s Theorem

Explanation from BOOK Relation between Speed and Pressure of Fluid


Explanation from BOOK Venturi Relation

Explanation from BOOK Blood Flow

Explanation from BOOK

6.6. A person is standing near a fast moving train. Is there any danger that he will fall towards it?

Yes, there is danger that he will fall towards the train. It is one of the applications of Bernoulli’s Equation. Explanation: When a train is moving fast, the velocity of air between the person and the train also increases as the train drags it. According to a result of Bernoulli’s equation, when the velocity of fluid increases, its pressure decreases. Thus, the pressure of the air between person and train decreases. The greater pressure behind the man may push him towards low-pressure side i.e. train. Therefore, there is a danger that he may fell towards it.

6.7. Identify the correct answer. What do you infer from Bernoulli’s theorem? (i) Where the speed of the fluid is high the pressure will be low. (ii) Where the speed of the fluid is high the pressure is also high. (iii) This theorem is valid only for turbulent flow of the fluid.

The correct answer is (i). Reason: According to the relation of Bernoulli’s equation,

6.8. Two row boats moving parallel in the same direction are pulled towards each other. Explain.

Two row boats moving parallel in the same direction are pulled towards each other. It is one of the applications of Bernoulli’s Equation. Reason: When the two row boats are moving parallel in the same direction, the velocity of the water flowing through them will be larger as compared to the rest of the water. According to the result of Bernoulli’s equation, the pressure of the water between the boats must decrease, as its velocity is large. As a result, the pressure of water on the outer sides is greater than inner side between the boats due to which the two boats are pulled towards each other.

6.9. Explain, how the swing is produced in a fast moving cricket ball.

It is one of the applications of Bernoulli’s Equation. Explanation: When a fast moving cricket ball moves in a such way that it spins as well as moves forward, the velocity of air on one side above the ball increases due to spin and air speed in the same direction below the ball and hence, the pressure decreases. According to Bernoulli’s equation, the pressure of the air below the ball is greater than that above the ball. The greater pressure on the other side below the ball deflects the path of ball and gives an extra curvature to the ball known as swing, which deceives the batsman.


6.10. Explain the working of a carburetor of a motor car using Bernoulli’s principle.

Working of carburetor: The carburetor of car engine uses a venturi duct to feed the correct mixture of air and petrol to the cylinders. Air passes through the duct and along a pipe to the cylinders. Petrol is mixed with air by a small valve at the side of duct. The air through the duct moves very fast which produces low pressure in the duct. It draws

petrol vapours into the air stream.

6.11. For which position will the maximum blood pressure in the body have the smallest value. (a) Standing up right (b) Sitting (c) Lying horizontally (d) Standing on one’s head?

The correct answer is (c). Explanation: Maximum blood pressure in the body has the smallest value when lying horizontally; because in this position, all the parts of the body will be in level with the heart. Thus, heart will not have to work hard as pumping against gravity. Moreover other options are incorrect because (a) Standing upright, systolic pressure has maximum value in the neck (c) Standing upright, systolic pressure has maximum value in the neck (d) In this case, the systolic pressure has maximum value in the legs

6.12. In an orbiting space station, would the blood pressure in major arteries in the leg ever be greater than the blood pressure in major arteries in the neck?

Blood pressure would be same. Reason: In an orbiting space station, everything is in state of weightlessness. Therefore, pressure will be same in major arteries of both in neck and legs.


CHAPTER 7: OSCILLATIONS

7.1. Name two characteristics of simple harmonic motion.

Simple harmonic motion (SHM) is a special kind of vibratory motion. Two characteristics of simple harmonic motion are given as below. i. Acceleration of a vibrating body is directly proportional to the displacement and is always

directed towards the mean position (or equilibrium position). i.e.

ii. Total energy of the particle executing SHM remains conserved. iii. SHM can be represented by a simple harmonic function of sine or cosine in the form of

equation, or Phase is a measure of how far the oscillator is away from its mean position at time t = 0.

7.2. Does frequency depends on amplitude for harmonic oscillators?

No, it does not depend upon amplitude of harmonic oscillator. Reason: As we know, the frequency of oscillation of simple pendulum is,

This relation shows that frequency does not depend upon the amplitude but it depends upon the length of pendulum and acceleration due to gravity. Similarly, in case of mass spring system, frequency of oscillation of mass is given by,

This relation shows that frequency does not depend upon the amplitude but it depends upon the mass of the body and spring constant ‘k’.

7.3. Can we realize an ideal simple pendulum?

No, we cannot realize an ideal simple pendulum. Reason: It is because for an ideal simple pendulum we must fulfill the following conditions.

i. Bob of very small size (point mass) must be used. ii. The suspension string must be weightless and inextensible.

iii. The bob of very small size (point mass) must be suspended from a rigid frictionless support. iv. Air also should be removed from the place of experiment.

These conditions could not be fulfilled 100%. Therefore, it is impossible to realize an ideal simple pendulum in nature.

7.4. What is the total distance traveled by an object moving with SHM in a time equal to its period, if its amplitude is A?

The total distance travelled by an object moving with SHM in its time period is equal to 4A, where A is an amplitude. Reason: Time period is a time during which the vibrating body completes one round trip. In one round trip, Total distance covered = A + A + A + A = 4A

A A


7.5. What happens to the period of a simple pendulum if its length is doubled? What happens if the suspended mass is doubled?

The time of simple pendulum is,

Here l is the length of simple pendulum and g is gravitational acceleration. Effect of Length:

When length is doubled, the time period is increased by . Proof If l = 2l, then from formula of simple pendulum,

Effect of Mass: When length is doubled, the time period remains same. Explanation As it is clear from the relation of time period of simple pendulum that it is independent of mass of the pendulum. Therefore, it does not change with the mass.

7.6. Does the acceleration of a simple harmonic oscillator remain constant during its motion? Is the acceleration ever zero? Explain.

No, the acceleration of harmonic oscillator does not remain constant during its motion. Reason: The magnitude of acceleration of a simple harmonic oscillator is given by,

where x is the displacement from the mean position. Since the displacement changes continuously during SHM, so its acceleration doe not remain constant. The value of acceleration at the mean position will be zero because at this position x = 0 and its maximum value will be at extreme positions because at this position x = xo.

7.7. What is meant by phase angle? Does it define angle between maximum displacement and the driving force?

Definition: The angle θ = ωt which specifies the displacement as well as the direction of motion of the point executing SHM is known as phase angle. Mathematical form: Mathematically, the phase angle is expressed as

θ = ωt where ω is angular frequency and t is any instant of time. It is the angle, which the rotating radius OP makes with reference direction OX at any instant t as shown in the figure. Importance: The phase determines the state of motion of the vibrating

point. If a body starts its motion from mean position, its phase at this point would be zero. Similarly, at extreme position, its phase would be π/2.

Phase angle simply tells us in what stage of vibration the simple harmonic oscillator is. It does not explain the angle between maximum displacement xo and the driving force.


7.8. Under what conditions does the addition of two simple harmonic motions produce a resultant, which is also simple harmonic?

In order to produce resultant SHM by the addition of two simple harmonic motions, following conditions must be fulfilled. Two SHMs must be parallel (i.e. their phases must be in the same direction). Two SHMs must have the same frequency (i.e. period) but different amplitudes. These two harmonic motions must have constant phase difference.

If two SHMs are given as,

Resultant SHM will be written as,

7.9. Show that in SHM the acceleration is zero when the velocity is greatest and the velocity is zero when the acceleration is greatest.

As the projection of a particle moving in a circle executes SHM, the following relations for velocity and acceleration are given as,

where x is instantaneous displacement, xo is the maximum displacement and ω is the constant of SHM called angular frequency. Case 1: Acceleration is zero when velocity is greatest. At the mean position, where x = 0

And

Case 2 : Velocity is zero when acceleration is greatest. At the extreme position, where x = xo

And

Conclusion: Hence, velocity is greatest and acceleration is zero at mean position. Hence, velocity is zero and acceleration is greatest at extreme position.

7.10. In relation to SHM, explain the equations; (i) y = A sin (ω t + ϕ ) (ii) a = - ω2x

(i) This equation represents the displacement of simple harmonic oscillator as a function of time. ϕ = initial phase angle which tells us the start of motion ωt = angle subtended in time t with angular frequency ω starting from initial phase ϕ (ωt is the

phase angle made with reference direction) y = instantaneous displacement of a particle performing SHM A = the amplitude of the oscillating particle

(ii) This equation represents the variation of acceleration in S.H. oscillator as a function of displacement. It tells us that the acceleration of the simple harmonic oscillator is directly proportional to its displacement and is directed towards the mean position. a = acceleration of a particle executing SHM ω = angular frequency of a particle x = instantaneous displacement of a particle from the mean position

7.11. Explain the relation between total energy, potential energy and kinetic energy for a body oscillating with SHM.

The total energy for the body oscillating with SHM always remains constant. Reason: For a body oscillating with SHM, the relation between potential energy, kinetic energy and total energy at any instant is,


Since total energy of SHM remains constant, therefore, any decrease in K.E. or P.E. results increase in P.E. or K.E. respectively.

At mean position, the energy is totally kinetic i.e. K.E. is maximum but P.E. is zero. At extreme position, the K.E. is totally changed into P.E. i.e. P.E. is maximum but K.E. is zero. At any point between mean and extreme position, total energy of simple harmonic oscillator is

sum of P.E. and K.E.

7.12. Describe some common phenomena in which resonance plays an important role.

Some of the common phenomena in which resonance plays an important role are;. 1. Microwave Oven: Resonance plays an important role in heating and cooking food by microwave oven. The microwaves produced by oven are absorbed due to resonance by water and fat molecules in the food. These waves have a wavelength of 12 cm and frequency of 2450 MHz .This increases the internal energy of the molecules. They get heat up and so food is cooked. 2. Tuning of Radio: Tuning of radio is a good example of electrical resonance. When we turn the knob of a radio, to tune a station, we are changing the natural frequency of the electrical circuit of the receiver until it becomes equal to the frequency of transmitter. When the two frequencies match, energy absorption is maximum and this is the only station we hear. 3. Motion of a swing: A swing is a good example of mechanical resonance. It is like a pendulum with a single natural frequency depending upon its length. If a series of regular pushes are given to the swing, its motion can be built up enormously. If pushes are given irregularly, the swing will hardly vibrate. 4. Musical Strings: In the musical strings when the frequency of enclosed air column wooden boxes under the strings becomes equal to the string frequencies to resonance, a loud sound of music is heard.

7.13. If a mass spring system is hung vertically and set into oscillations, why does the motion eventually stop?

If a mass spring system is hung vertically and set into oscillations, the motion eventually stops. Reason: It is because the amplitude of the oscillating system becomes smaller and smaller with the passage of time. Finally, the oscillations of mass-spring system stop due to friction, air resistance and some other damping force. Thus, mechanical energy of the system is wasted into heat due to the resistive forces. Such an oscillator can be called as damped harmonic oscillator.


CHAPTER 8: WAVES

8.1. What features do longitudinal waves have in common with transverse waves?

Longitudinal waves: Those waves in which the particles of the medium have displacements along the direction of propagation of waves are called longitudinal waves. It is made up of rarefactions and compressions. Transverse waves: Those waves in which particles of medium are displaced in a direction perpendicular to the direction of propagation of waves are called transverse waves. It is made up of crests and troughs. Common features: The longitudinal waves have following features in common with the transverse waves,

i. In both type of waves, the particles oscillate (vibrate) about their mean position. ii. Both of the waves require medium for their propagation.

iii. Both type of waves transport energy from one place to another but do not matter. iv. In both type of waves, the relation between frequency, wavelength and speed of waves is given

by v = fλ. v. Both are mechanical waves.

vi. Stationary waves can be studied in both types of waves. vii. Both type of waves produce disturbances in the medium through which they pass.

viii. The velocity of propagation in both types of waves depends on the elasticity and inertia of a medium.

8.2. The five possible waveforms obtained when the output from a microphone is fed into the Y-input of cathode ray oscilloscope, with the time base on, are shown in the fig. These waveforms are obtained under the same adjustment of the cathode ray oscilloscope controls. Indicate the waveform

A B C D E (a) Which trace represents the loudest note? (b) Which trace represents the highest frequency?

(a) Trace D has loudest note because loudness depends on the amplitude of vibration and in trace D amplitude in highest.

(b) Highest frequency depends on the large number of waves per second. Thus, trace B represents highest frequency.

8.3. Is it possible for two identical waves travelling in the same direction along a string to give rise to a stationary wave?

No, it is not possible for two identical waves travelling in same direction along the string to give rise to a stationary wave. Reason: Stationary waves are produced only when two identical waves travelling in opposite direction along the string.


8.4. A wave is produced along a stretched string but some of its particles permanently show zero displacement. What type of wave is it?

These are stationary or standing waves. Reason: Only in stationary waves some points of the medium permanently show zero displacement called nodes and some point shown maximum displacement called antinodes.

8.5. Explain the terms crest, trough, node and antinode.

Crest: In transverse waves, the portion of medium above its mean level (equilibrium position) is called crest. Trough: In transverse waves, the portion of medium below its mean level (equilibrium position) is called trough. Node: In stationary wave, the point where the strain is maximum and amplitude (displacement) is zero is called node. Antinode: In stationary wave, the point where the strain is minimum and amplitude (displacement) is maximum is called node.

8.6. Why does sound travel faster in solids than in gases?

The speed of sound in solids is about 1500 times more than as in gases. Reasons: The speed v of sound in a medium of modulus of elasticity E and density ρ is given by,

In the case of solids, E is taken as its Young’s modulus (modulus of elasticity) while in the case of gas E is taken as its bulk modulus. It is true that the density of solids is larger than that of gases, but at the same time, Young’s modulus of solids is far greater than the bulk modulus of a gas (i.e. Es>> Eg). Therefore, the ratio E/ρ is much larger for solids than in gases. Hence, the speed v of sound is greater in solid than in gas. In other words, sound travels faster in solids than in gases.

8.7. How are beats useful in tuning musical instruments?

Beats are very useful in tuning musical instruments. Explanation: We know that the number of beats produced per second is equal to difference between the frequencies of two surrounding bodies. By tuning musical instrument, we mean to set it to produce a note (sound) of desired frequency. For this purpose, we take a standard instrument of known frequency. The unturned musical instrument and the standard instrument are sounded together. At first, the number of beats will be produced due to slightly frequency difference between them. The frequency of the musical instrument is gradually adjusted until the number of beats becomes

equal to zero. When this happens, the musical instrument will produce the note of desired frequency and is said

to be tuned. In this way, beats become useful in tuning a musical instrument.


8.8. When two notes of frequencies f1 and f2 are sounded together, beats are formed. If f1 > f2 , what will be the frequency of beats? (i) f1 + f2 (ii) ½ (f1 + f2 ) (iii) f1 - f2 (iv) ½ (f1 - f2 )

The correct answer is (iii) Reason: The frequency of beats will be f2 – f1 because number of beats per second is equal to the difference between the frequencies of two sounding bodies.

8.9. As a result of distant explosion, an observer senses a ground tremor and then hears the explosion. Explain the time difference.

As a result of distant explosion, an observer senses a ground tremor and then hears the explosion. Explanation: The speed v of sound in a medium of modulus of elasticity E and density ρ is given by,

As, the explosion occurs, the disturbances in the medium (air) are produced. Some of them travel through air while the other passes through the ground. Since, the speed of sound in solids (earth) is greater than the speed of wave in gases (air) due to much greater value of elastic modulus. That is why the observer senses the ground tremor first and then hears the explosion. The time difference is due to different speed of waves in two different mediums.

8.10. Explain why sound travels faster in warm air than in cold air.

Sound travels faster in warm air than in cold air. Explanation: The speed v of sound in a medium of modulus of elasticity E and density ρ is given by,

The relation shows that speed is inversely proportional to the density i.e. v α 1/ρ. It means greater the density, smaller the speed of sound. However, the density decreases with the rise in temperature i.e. ρ α 1/T. In the case of warm air, since temperature is greater so the density is smaller. Hence, the speed of

sound increases. In the case of cold air, since the temperature is smaller so the density is larger. Hence, the speed

of sound decreases. Therefore, it is concluded that sound travels faster in warm air than in cold water.

8.11. How should a sound source move with respect to an observer so that the frequency of its sound does not change?

If the relative velocity between the source and the observer is zero, there will be no change in frequency of sound. Explanation: According to the Doppler’s Effect, the apparent change in frequency of sound is produced due to relative motion of the source of sound and observer. If sound source and observer move in such a way that their relative velocity is zero, then the apparent frequency of the sound does not change. In other words, we can say that if sound source and observer move with same velocity along the same direction there will be no change in frequency of sound due to zero relative velocity.


CHAPTER 9: PHYSICAL OPTICS

9.1. Under what conditions two or more sources of light behave as coherent sources?

Conditions: Under following conditions two or more sources of light behave as coherent sources;

i. If they emit continuously light waves of the same amplitude, same time period and same frequency (or wavelength)

ii. If the emitted waves have same phase or constant phase difference. iii. If two sources of light, have zero phase difference or constant phase difference. iv. If two sources must be close to each other. Method of Production: A common method of producing two coherent light sources is to use a single source to illuminate a screen containing two narrow slits. Thus, two or more sources derived from a single source of light will behave as coherent sources, because they are in the same phase.

9.2. How is the distance between interference fringes affected by the separation between the slits of Young’s experiment? Can fringes disappear?

By increasing the separation between slits, fringe spacing is decreased and vice versa. Reason: The formula for fringe spacing is given by,

This relation shows that the fringe spacing ∆y varies inversely with the slit separation d. Fringes Disappearing: It means that greater the separation between the slits, the smaller will be the fringe spacing. When the separation between the slit is made large enough, the fringes will be so close that they cannot be distinguished and will disappear on further increase of slit separation d.

9.3. Can visible light produce interference fringes? Explain.

Yes, the visible light or white light can produce interference fringes. Explanation: As visible light is a mixture of seven component colours so each component colour will produce interference fringes corresponding to its own wavelength. Hence, the fringes pattern will be coloured. However, the fringes will overlap due to different wavelengths of the colours, so it would be difficult to observe the interference fringes of visible or white light.


9.4. In the Young’s experiment, one of the slits is covered with blue filter and other with red filter. What would be the pattern of light intensity on the screen?

No interference pattern of bright and dark fringes is formed on screen. Conditions of Interference: Following are the important conditions for the interference of the light waves,

i. The interference fringes must be monochromatic i.e. of a single wavelength. ii. The interfering beams of light must be coherent.

Following are the other necessary conditions, iii. The sources should be narrow and very close to each other. iv. The intensity of the two sources must be comparable. Explanation: As the condition of the interference of the light waves is not fulfilled i.e. being monochromatic. Red and blue lights have different wavelengths due to which there will be no maxima or minima on the screen. We shall observe two coloured images on the screen with constant intensity.

9.5. Explain whether the Young’s experiment is an experiment for studying interference or diffraction effects of light.

Basically, it is an experiment to study interference of light though it involves diffraction. Explanation: Young’s experiment is basically used to study interference effects of light. However, the spreading of light waves around the edges of the slits also produces some diffraction effects but interference phenomenon plays a prominent role than the diffraction phenomenon. Since diffraction occurs along with the interference in the experiment, therefore, the same experiment is also used to study diffraction effect. However, diffraction is a special type of interference, s interference phenomenon has upper hand upon the diffraction phenomenon.

9.6. An oil film spreading over a wet footpath shows colours. Explain how does it happen?

The colours are seen on the oil film spreading over a wet footpath due to interference of light waves. Explanation: If white light is incident on an oil film of irregular thickness at all possible angles, we should consider the interference pattern due to each spectral colour separately. It is quite possible that at a certain place on the film, its thickness and the angle of incidence of light are such that the condition of destructive interference of one of seven colours is being satisfied.

Hence, this one colour is disappeared and that portion of the film will exhibit the remaining constituent colours of the white light (six colours).

9.7. Could you obtain Newton’s rings with transmitted light? If yes, would the pattern be different from that obtained with reflected light?

Yes, Newton’s Rings can be observed with transmitted light. Explanation: In case, of transmitted light, the fringe pattern is just opposite to the reflected light because of no phase change of 180°. It means that the central spot of Newton’s Rings in this case will be bright instead of dark due to the transmitted light.


9.8. In the white light spectrum obtained with a diffraction grating, the third order image of a wavelength coincides with the fourth order image of a second wavelength. Calculate the ratio of the two wavelengths.

The grating equation is given by,

For first wavelength n = 3 (as it is third order image) λ = λ1

then equation (I) can be written as,

For second wavelength n = 4 (as it is fourth order image) λ = λ2

then equation (I) can be written as,

Comparison: Comparing equation (II) and (III)

Hence, the ratio of two wavelengths is 4 : 3 or 1.33:1.

9.9. How would you manage to get more orders of spectra using a diffraction grating?

By increasing the grating element d (or decreasing the number of rulings) and using the light whose wavelength λ is small. Explanation: As the formula of diffraction grating is,

then,

for a given wavelength λ, the order of spectra depends upon d, that is, n is directly proportional to d i.e.

but

here N is the number of rulings on the grating. Then from (I) and (II),

Hence from (III), it is concluded that; i. The maximum value of sin θ = 1

ii. In order to get more spectra, we should increase the grating element d i.e. spacing between the lines on grating or decrease the number of rulings N on the grating.

iii. In order to get more spectra, we should decrease the wavelength of monochromatic light.


9.10. Why the polaroid sunglasses are better than ordinary sunglasses?

Polaroid sunglasses are better than ordinary sunglasses. Explanation: The sunlight reflected from water, glass and rough road surfaces, for large angle of incidences, is partially polarized and so it produces glare. Glare can be reduced by using polaroid sunglasses because they decrease the intensity of light passing through them. In this way, our eye is saved from unnecessary strain of glare. Hence, the polaroid sunglasses are better than ordinary sunglasses because the ordinary sunglasses cannot provide much less intensity of light.

9.11. How would you distinguish between un-polarized and plane-polarized lights?

Difference between Un-Polarized and Plane Polarized Velocity:

Un-Polarized Lights Plane Polarized Lights

Definition: The beam of ordinary light consisting of large number of planes of vibration is called un-polarized light.

Definition: The beam of light in which all vibrations are confined to a single plane of vibration is called un-polarized light.

Planes of Vibration: Light travels in random planes.

Planes of Vibration: Light travels in only one plane.

Example: Light emitted by sun.

Example: Light emitted by laser light.

A Polaroid will distinguish between un-polarized and plane-polarized light. If a Polaroid is rotated in front of un-polarized light, a component of light will pass for each angle. However, for plane-polarized light, at certain orientation, no light will pass.

9.12. Fill the blanks.

(i) According to Huygens’s principle, each point on a wave front acts as a source of secondary wavelets.

(ii) In Young’s experiment, the distance between two adjacent bright fringes for violet light is smaller than that for green light.

(iii) The distance between bright fringes in the interference pattern increases as the wavelength of light used increases.

(iv) A diffraction grating is used to make a diffraction pattern for yellow light and then for red light. The distances between the red spots will be greater than that for yellow light.

(v) The phenomenon of polarization of light reveals that light waves are transverse waves. (vi) A polaroid is a commercial polarizer.

(vii) A polaroid glass reduces/eliminates glare of light produced at a road surface.


CHAPTER 10: OPTICAL INSTRUMENTS

10.1. What do you understand by linear magnification and angular magnification? Explain how a convex lens is used as a magnifier?

Linear Magnification Definition: “It is defined as the ratio of the size of the image to the size of the object.” OR “It is defined as the ratio of distance of image from lens to distance of object from lens.” Units: It has no units but only a simple number because this is the ration between two similar quantities. Formula:

Angular Magnification Definition: It is defined as the ratio of the angles subtended by the image as seen through the optical device to that subtended by the object at the unaided eye. Units: It has no units but only a simple number because this is the ration between two similar quantities.

Formula:

Convex lens as Magnifier A convex lens of short wavelength can be used as a magnifier when the object is placed much closed to it i.e. when we place the object within the focal length of lens. Thus, image formed is virtual, erect, and magnified.

10.2. Explain the difference between angular magnification and resolving power of an optical instrument. What limits the magnification of an optical instrument?

Difference between Angular Magnification and Resolving Power:

Angular Magnification Resolving Power

Definition: It is defined as the ratio of the angles subtended by the image as seen through the optical device to that subtended by object at the unaided eye.

Definition: The resolving power of an instrument is its ability to resolve the minor details of the object under examination.

Formula:

Formula:

Limitations of Magnification: The magnification of the optical lenses is limited due to defects of the lens such as chromatic and spherical aberrations. The image does not remain well defined and details of the objects cannot be seen clearly. These defects are defined below:


(i) Chromatic Aberrations In optics, chromatic aberration (CA, also called achromatism, chromatic distortion, and spherochromatism) is a type of distortion in which there is a failure of a lens to focus all colors to the same convergence point.

(ii) Spherical Aberrations

Spherical aberration is an optical effect observed in an optical device (lens, mirror, etc.) that occurs due to the increased refraction of light rays when they strike a lens or a reflection of light rays when they strike a mirror near its edge, in comparison with those that strike nearer the centre. It signifies a deviation of the device from the norm, i.e., it results in an imperfection of the produced image.

10.3. Why would it be advantageous to use blue light with a compound microscope?

It would be advantageous to use blue light with a compound microscope. Reason: As we know,

Also,

An objective lens of large aperture and use of blue light of short wavelength produces less diffraction and increases its resolving power. Thus, the eye can see more details of an object.

10.4. One can buy a cheap microscope for use by the children. The image seen in such a microscope have coloured edges. Why is this so?

One can buy a cheap microscope for use by the children. The image seen in such a microscope have coloured edges. Reason: It is due to chromatic aberration. Chromatic aberration is a type of distortion in which there is a failure of a lens to focus all colors to the same convergence point. The white light will disperse after passing through the lenses. Such lenses cannot bring all the rays of white light from the object to a single point (focal point) which will give coloured image.


10.5. Describe with the help of diagrams, how (a) a single biconvex lens can be used as a magnifying glass. (b) biconvex lenses can be arranged to form a microscope.

Simple Microscope: The object is placed between the lens and focus.

Compound Microscope: The object of height h is placed just beyond the principal focus of the objective. This produces the real, magnified image of height h1 inside the focal length of eyepiece. The eyepiece further magnifies it.

10.6. If a person were looking through a telescope at the full moon, how would the appearance of the moon be changed by covering half of the objective lens?

The apparent size of the image of the moon does not change. It looks dim only. Reason: If half of the objective lens of a telescope is covered, the moon will appear full to the person looking at it. However, the intensity of light depends upon the diameter of the erect lens; therefore, the intensity of light received from the moon will decrease. Thus, its brightness is reduced by the half-covered telescope.

10.7. A magnifying glass gives a five times enlarged image at a distance of 25 cm from the lens. Find, by ray diagram, the focal length of the lens.

Ray Diagram:


Focal Length: As, M = 5 and d = 25 cm

cm

Hence, the focal length of lens is 6.25 cm.

10.8. Identify the correct answer. (i) The resolving power of a compound microscope depends on;

(a) The refractive index of the medium in which the object is placed. (b) The diameter of the objective lens. (c) The angle subtended by the objective lens at the object. (d) The position of an observer’s eye with regard to the eye lens.

(ii) The resolving power of an astronomical telescope depends on: (a) The focal length of the objective lens. (b) The least distance of distinct vision of the observer. (c) The focal length of the eye lens. (d) The diameter of the objective lens.

(i) The resolving power of a lens of diameter D is given by

Hence, correct answer is (b). (ii) The resolving power of a lens of diameter D is given by

Hence, correct answer is (d).

10.9. Draw sketches showing the different light paths through a single-mode and multi-mode fibre. Why is the single-mode fibre preferred in telecommunications?

Sketches:


Preference of Single Mode Step Index Fibre: Size: It has very thin core of 5 μm dameetr and has a relatively larger cladding of glass or plastic. Source of Transmission: It has a very thin core, a strong monochromatic light source i.e. a laser source has to be used to send light signal through it. Uses: it can carry more than 14 TV channels or 14000 phone calls. That’s why the single-mode fibre is preferred in telecommunications.

10.10. How the light signal is transmitted through the optical fibre?

For Extensive Question

Light signal is transmitted by: (i) Total Internal Reflection (FOR EXPLANATION CONSULT TEXTBOOK)

Definition Index of Refraction Refraction Critical Angle (FIGURE) Snell’s Law (FIGURE) Critical Angle for Glass (FIGURE) Axial Rays

(ii) Continuous Refraction (FOR EXPLANATION CONSULT TEXTBOOK)

Multimode Step Index Fibre (FIGURE) Multimode Graded Index Fibre (FIGURE) Propagation of Light (FIGURE)

For Short Question

Light signal are transmitted through the optical fibre by: 1. Transmitter: It converts electrical signal to light signal. 2. Optical Fibre: it is used for guiding the signal by total internmal reflection and continuous

refraction. 3. Receiver: it converts light signal to electrical signal and then to sound

10.11. How the power is lost in optical fibre through dispersion? Explain.

When light signal is not perfectly monochromatic, then light will disperse on passing through the core of the optical fibre into the different wavelengths λ1, λ2 and λ3 etc. Each wavelengths meets core-cladding boundary at different critical angles. Each wavelength has different path length. Therefore, the light of different wavelengths reaches the other end of fibre at different times. Therefore, the signal received is distorted or faulty.


CHAPTER 11: HEAT AND THERMODYNAMICS

11.1. Why is the average velocity of the molecules in a gas zero but the average of the square of velocities is not zero?

Average velocity of the molecules in a gas zero but the average of the square of velocities is not zero. Reason: There are a large number of molecules in a gas. According to our assumption, equal number of molecules move in all directions. It means that the

number of molecules moving to the right in x-direction is equal to the number of molecules moving to the left in the opposite direction with the same velocity. Thus, the vector sum of their velocities will be zero.

But the square of the negative velocity i.e. [(-v)2 = v2] is also a positive, therefore the average of the square of the velocities will not be zero.

11.2. Why does the pressure of a gas in a car tyre increase when it is driven through some distance?

The pressure of a gas in a car tyre increase when it is driven through some distance. Reason: When a car driven through small distance, work done by the car is partly spent in overcoming the frictional force between the road and the car tyre. Some part of work done against friction is converted into heat which raises the temperature of the gas in a car tyre. As we know that pressure is directly proportional to the absolute temperature at constant volume, therefore the pressure must increase because the heat energy increases the velocity and collisions of gas molecules. As a result, molecular collisions against the walls of a tyre increase the pressure of air inside the tyre.

11.3. A system undergoes from state P1 V1 to state P2 V2 as shown in the fig. What will be the change in internal energy?

The change in internal energy of the system is zero. Reason: It is clear from the figure that temperature of the system is constant. It means that internal energy is also constant as it depends upon temperature. Therefore, there will be no change in internal energy.

11.4. Variation of volume by pressure is given in the fig. A gas is taken along the paths ABCDA, ABCA and A to A. What will be the change in internal energy?


The change in internal energy of the system is zero in all cases. Reason: It is clear from the figure that temperature of the system is constant. It means that internal energy is also constant as it depends upon temperature. Therefore, there will be no change in internal energy.

11.5. Specific heat of a gas at constant pressure is greater than specific heat at constant volume. Why?

Specific heat of a gas at constant pressure is greater than specific heat at constant volume. Reason: When a gas is heated at constant pressure, then the heat supplied is used in two ways,

i. Some part of heat is used in doing the external work to move the piston up against the constant atmospheric pressure.

ii. The other part of heat is used to increase the internal energy and temperature. If the same gas is heated at constant volume, no external work is done to expand the gas. The

total heat supplied is used to increase the internal energy and temperature of the gas. This shows that more heat is required to heat the gas at constant pressure than at constant volume for the same rise of temperature.

So we conclude that specific heat at constant pressure is greater than the specific heat at constant volume i.e. Cp > Cv.

11.6. Give an example of a process in which no heat is transferred to or from the system but the temperature of the system changes.

Adiabatic process is an example of such a process. Adiabatic Process: Definition: An adiabatic process is the one in which no heat enters or leaves the system. Explanation: Therefore, Q = 0 and the first law of thermodynamics gives,

W = -∆U Thus if the gas expands and does external work, it is done at the expense of the internal energy of its molecules and hence, the temperature of the gas falls. Conversely, an adiabatic compression causes the temperature of the gas to rise because of the work done on the gas. This change occurs when the gas expands or is compressed rapidly, particularly when the gas is contained in an insulated cylinder. Examples: The examples of adiabatic process are,

The rapid escape of air from a burst tyre The rapid expansion and compression of air through which ha sound wave is passing Cloud formation in the atmosphere

γ: In case of adiabatic changes it has been seen that,

PVγ = constant Where, γ is the ratio of the molar specific heat of the gas at constant pressure to the molar specific heat at constant volume i.e.

Adiabat: The curve representing the adiabatic process is called adiabat.


11.7. Is it possible to convert internal energy into mechanical energy? Explain with example.

Yes, it is possible to convert internal energy into mechanical energy. Explanation: Applying the first law of thermodynamics to an adiabatic process,

In such process, ∆Q = 0 then,

If work done, ‘∆W’ is negative, then the work is done at the cost of internal energy. This means if a system is allowed to expand adiabatically, some work is done at the cost of internal energy. Thus internal energy decreases because some quantity of internal energy has been converted into mechanical work. Examples: Gases can be liquefied by this process In case of heat engines (e.g. petrol engine), the hot gases expand and the piston moves backward.

In this way, also internal energy is converted into work (i.e. mechanical energy).

11.8. Is it possible to construct a heat engine that will not expel heat into the atmosphere?

No, it is not possible to construct a heat engine that will not expel heat into the atmosphere. Reason: According to Newton’s second law of thermodynamics, all the practical heat engines absorb heat from the source, convert a part of its into mechanical work and reject the remainder to the cold body or atmosphere. Hence, no heat engine can operate with a single source for conversion of heat into mechanical work without expelling heat to the atmosphere. In other words, there must be a temperature difference between the hot and cold bodies (source and sink) for the conversion of heat into mechanical work.

11.9. A thermos flask containing milk as a system is shaken rapidly. Does the temperature of milk rise?

Yes, the temperature of milk rises. Reason: As we know

Hence, when the milk is shaken rapidly, the kinetic energy of the molecules of the milk increases, which causes an increase in the temperature and internal energy. No heat is added to the milk. While we are shaking milk, we do some work on it, which is converted into kinetic energy of molecules of milk.

11.10. What happens to the temperature of the room, when an air conditioner is left running on a table in the middle of the room?

The temperature of the room will not decrease but it increase slightly. Reason: As the running air conditioner is placed on a table in the middle of the room, rejects the heat through the compressor in the same room. Thus, no change in the room temperature occurs because the heat absorbed from the room is expelled or lost in the same room. There are two cases

In ideal cases, the room temperature remains constant. In non- ideal case, the room temperature slightly increases.

Hence, there will be no effect on the temperature of the room but it slightly increases.


11.11. Can the mechanical energy be converted completely into heat energy? If so, give an example.

Yes, the mechanical energy can be completely converted into heat energy. Explanation: When work (mechanical energy) is done in compressing the gas by adiabatic process, the increase in the internal energy ∆U of the gas is equal to the work done W on it. Applying the first law of thermodynamics to an adiabatic process,

But, Q = 0 and W = negative (work against on gas) then,

The whole of the mechanical energy can be absorbed by the molecules of the gas in the form of their K.E. This K.E. gets converted into heat. Examples: When brakes of speeding car are applied, it stops which means that all of its K.E. is converted into

heat. Second law of thermodynamics does not apply when work is being converted into heat. If we rub our hands, by rubbing them the whole mechanical energy converted into heat energy.

11.12. Does entropy of a system increase or decrease due to friction?

The entropy of system increases due to friction. The measure of increase in disorder of a thermodynamic system or degradation of energy is called entropy. Reason: If the work done by friction, the work will be converted into heat. The heat produced due to the friction goes into the surrounding i.e. air and becomes useless. No useful work can be performed by it due to the unavailability of this energy; we can say that the entropy will increase when work is done by friction. Hence, the entropy of system increases due to friction.

11.13. Give an example of a natural process that involves an increase in entropy.

The measure of increase in disorder of a thermodynamic system or degradation of energy is called entropy. Example: When ice melts due to temperature of its surroundings, it is converted into water. The heat ∆Q transferred to ice from surroundings at absolute temperature t is positive. Thus, entropy of melted ice (i.e. water) increases by the following equation,

As ∆S is positive, therefore the entropy of this natural process (i.e. melted ice) increases. All natural processes in which friction is involved, the entropy of the system increases, Free expansion of gas Transfer of heat from sun to earth Blow of wind Rubbing your hands together in cold Propagation of sound through air

11.14. An adiabatic change is the one in which a. No heat is added to or taken out of a system b. No change of temperature takes place c. Boyle’s law is applicable d. Pressure and volume remains constant

Statement (a) is correct Reason: It is because an adiabatic change is one in which no heat is added or taken out of a system.

11.15. Which one of the following process is irreversible? a. Slow compressions of an elastic spring b. Slow evaporation of a substance in an isolated vessel c. Slow compression of a gas d. A chemical explosion


Statement (d) is correct Reason: It is because a chemical explosion cannot be reversed. Hence it is an adiabatic change.

11.16. An ideal reversible heat engine has a. 100% efficiency b. Highest efficiency c. An efficiency, which depends on the nature of working substance d. None of these.

Statement (b) is correct Reason: According to second law of thermodynamics, the efficiency of a heat engine cannot be 100%. Hence, an ideal heat engine has highest efficiency.

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Physics XI-Short Questions