Engineering Mechanics_course File

Engineering Mechanics (Online Questions)

First Unit

1. A barge is pulled by 2 huge boat. If the resultant force exerted by the tugboats is

5000 N directed along the axis of the barge, determine the value of for which the

tension in rope 2 is minimum

Correct Response: 60 deg Distractor 1: 30 deg Distractor 2: 90 deg Distractor 3: 180 deg Distractor 4: 45 deg Distractor 5: 270 deg

2. A man pulls with a force of 300 N on a rope attached to a building, as in figure. What are the horizontal and the vertical components of the force (vectorial representation) exerted by the rope at point A?

Correct Response: 240i - 180j Distractor 1: 240i + 180j Distractor 2: 180i - 240j

Distractor 3: 180i + 240j Distractor 4: -240i - 180j Distractor 5: -180i - 240j

3. When a system of non-concurrent forces are acting on a body, then they are solved by using which law

Correct Response: none of the options Distractor 1: polygon law Distractor 2: triangular law Distractor 3: parallelogram law Distractor 4: all the options are correct Distractor 5: newtons law

4. When a body is in equilibrium, then which of the following statement is not false

1) the body is travelling with uniform acceleration

2) the body is at rest

3) the body is travelling with uniform velocity

4) the body is travelling with non-uniform acceleration

5) the body is travelling with non-uniform velocity

Correct Response: 1 & 2 Distractor 1: 1 & 3 Distractor 2: 1 & 4 Distractor 3: 1 & 5 Distractor 4: 2 & 4 Distractor 5: none of the options

5. A member BD exerts on member ABC a force Q directed along BD. Knowing that P must have a 300 N horizontal component, find the magnitude of the force P.

Correct Response: 523 N Distractor 1: 500 N Distractor 2: 423 N Distractor 3: 400 N Distractor 4: 323 N Distractor 5: 300 N

6. Which of the following is true with respect to engineering mechanic

Correct Response: a system of non-concurrent can be solved using classical approach Distractor 1: a system of non-concurrent cannot be solved using classical approach Distractor 2: free body diagram is drawn based on continuum hypothesis Distractor 3: in free body diagram intermolecular forces are considered Distractor 4: none of the options

Distractor 5: all the options

7. What do you mean by coplanar forces?

Correct Response: Forces which lies in one plane Distractor 1: Forces which lies in two plane Distractor 2: Forces which lies in one or more planes Distractor 3: Forces which lies in the surface Distractor 4: Concurrent forces are also called as co-planar forces Distractor 5: none of the options

8. Which of the following is a scalar quantity?

Correct Response: none of the options Distractor 1: Force Distractor 2: Velocity Distractor 3: Acceleration Distractor 4: Moment Distractor 5: Torque

9. A force F has the components Fx = 150 N, Fy=-200 N, Fz=300 Determine the magnitude F

Correct Response: 390.51 N Distractor 1: 367.78 N Distractor 2: 237.75 N Distractor 3: 563.11 N Distractor 4: 765.97 N Distractor 5: 635.98 N

10. Mass of 1 kg attached to the middle of a rope, which is being pulled from both its end in opposite direction. Taking g = 9.81 m/s2 , the minimum pull required so that the ropes are straight is

Correct Response: Infinity Distractor 1: 132 kN Distractor 2: 50 kN Distractor 3: 0 kN N Distractor 4: 450 kN Distractor 5: the question provided is wrong

11. What do you mean by coplanar forces?

Correct Response: Forces which lies in one plane Distractor 1: Forces which lies in two plane Distractor 2: Forces which lies in one or more planes Distractor 3: Forces which lies in the surface Distractor 4: none of the options

Distractor 5: Forces that are present in two dimension

12. The joint O of a space frame is subjected to four forces. Strut OA lies in the x-y plane and strut OB lies in the y-z plane. Determine the force acting in each if the three struts required for equilibrium of the joint. Set = 45.

Correct Response: F = 56.6 lb, R = 424 lb, P = 1000 lb Distractor 1: F = 46.4 lb, R = 400 lb, P = 424 lb Distractor 2: F = 11.3 lb, R = 424 lb, P = 577 lb Distractor 3: F = 1166 lb, R = 424 lb, P = 1000 lb Distractor 4: none of the options Distractor 5: F = 1266 lb, R = 424 lb, P = 1000 lb

13. If the resultant of two equal forces has the same magnitude as either of the forces, then the angle between the two forces is

Correct Response: 120 Distractor 1: 30 Distractor 2: 60 Distractor 3 90 Distractor 4: 45 Distractor 5: 180

14. If the masses of both the bodies, as shown in the below figure, are reduced to 50 percent, then tension in the string will be

Correct Response: 1/2 Distractor 1: same Distractor 2: twice Distractor 3 thrice Distractor 4: 1/3 Distractor 5: none of the options

15. The figure shows the two equal forces at right angles acting at a point. The value of force R acting along their bisector and in opposite direction is

Correct Response: Distractor 1: P/2 Distractor 2: 2P

Distractor 3 Distractor 4: P Distractor 5: none of the options

16. Determine the angle :

Correct Response: 50 Distractor 1: 40 Distractor 2: 30 Distractor 3: 60 Distractor 4: 70 Distractor 5: none of the options

17. The algebraic sum of the resolved parts of a number of forces in a given direction is equal to the resolved part of their resultant in the same direction. This is known as

Correct Response: principle of resolution of forces Distractor 1: principle of independence of forces Distractor 2: principle of transmissibility of forces Distractor 3: parallelogram law of forces Distractor 4: triangular law of force Distractor 5: none of the options

18. The angle between two forces when the resultant is maximum and minimum respectively are

Correct Response: 0 and 180 Distractor 1: 180 and 0 Distractor 2: 90 and 180 Distractor 3: 90 and 0 Distractor 4: 90 and 45 Distractor 5: 45 and 90

19. The minimum force required to slide a body of weight W on a rough horizontal plane is

Correct Response: W tan Distractor 1: W sin Distractor 2: W cos Distractor 3: Since the force are perpendicular, they cant be related Distractor 4: Weight has no effect on the force applied Distractor 5: none of the options

20. In a framed structure, as shown in the below figure, the force in the member BC is

Correct Response: 2W/3 (tension) Distractor 1: 2W/3 (compression) Distractor 2: W/3 (compression) Distractor 3: W/3 (tension) Distractor 4: W/2 (tension) Distractor 5: W/2 (compression)

21. The resultant of two forces P and Q acting at an angle is

Correct Response: (2 + 2 + 2

Distractor 1: (2 + 2 2

Distractor 2: (2 + 2 2

Distractor 3: (2 + 2 + 2

Distractor 4: P2 + Q2 + 2PQcos3

Distractor 5: P2 + Q2 2PQcos3

22. Non-coplanar concurrent forces are those forces which

Correct Response: meet at one point, but their lines of action do not lie on the same plane Distractor 1: do not meet at one point and their lines of action do not lie on the same plane Distractor 2: meet at one point and their lines of action also lie on the same plane Distractor 3: do not meet at one point, but their lines of action lie on the same plane Distractor 4: do not meet at one point, and their lines of action do not lie on the same plane Distractor 5: none of the options

23. In the shown figure, the tension (T) in the string will be

Correct Response: 212

1+2

Distractor 1: 12

1+2

Distractor 2: 1+2

12

Distractor 3: 12

12

Distractor 4: they cant be related Distractor 5: none of the options

24. The resultant of the two forces P and Q is R. If Q is doubled, the new resultant is perpendicular to P. Then

Correct Response: Q=R Distractor 1: P=Q Distractor 2: Q=2R Distractor 3: P=2R Distractor 4: P=R Distractor 5: P=2Q

25. The resultant of two forces P and Q (such that P > Q) acting along the same straight line, but in opposite direction, is given by

Correct Response: P-Q Distractor 1: P+Q Distractor 2: P/Q Distractor 3: Q/P Distractor 4: P-2Q Distractor 5: P+2Q

26. The law of motion involved in the recoil of gun is

Correct Response: Newton's third law of motion Distractor 1: Newton's first law of motion Distractor 2: Newton's second law of motion Distractor 3: Newton's second law of gravity Distractor 4: Ohm's law Distractor 5: none of these

27. The resultant of two equal forces P making an angle , is given by

Correct Response: 2

2

Distractor 1: 2

2

Distractor 2: 2

2

Distractor 3: 2

2

Distractor 4: 2

2

Distractor 5: none of these

28. The force induced in the string AB due to the load W, as shown in the below figure is

Correct Response: W cosec Distractor 1: W sin Distractor 2: W cos Distractor 3: W sec Distractor 4: W tan Distractor 5: W cot

29. One kilogram is equivalent to Newton

Correct Response: 9.81N Distractor 1: 1N Distractor 2: 1.5N Distractor 3: 20N Distractor 4: 15N Distractor 5: none of the options

30. The resolved part of the resultant of two forces inclined at an angle in a given direction is equal to

Correct Response: the algebraic sum of the resolved parts of the forces in the given direction Distractor 1: the sum of the resolved parts of the forces in the given direction Distractor 2: the difference of the forces multiplied by the cosine of Distractor 3: the sum of the forces multiplied by the sin of Distractor 4: the sum of the forces multiplied by the angle Distractor 5: none of the options

Second Unit

1. Determine the magnitude and direction of the moment of the force of the

movement if the force at A about point P.

Correct Response: Mp = 400 Nm

Distractor 1: Mp = 400 Nm





2. Replace the force at A by an equivalent force and couple moment at P.

Correct Response: F = 15 kN @ = 36.9 , Mp = 67.1 kN-m

Distractor 1: F = 15 kN @ = 36.9 , Mp = 30 kN-m

Distractor 2: F = 15 kN @ = 143.1 , Mp = 67.1 kN-m

Distractor 3: F = 15 kN @ = 143.1 , Mp = 30 kN-m

Distractor 4: F = 15 kN @ = 143.1 , Mp = 67.1 kN-m Distractor 5: none of the options

3. Identify the which of the following statement is not correct

a. Two parallel forces of same magnitude is called couple b. Two parallel forces of same magnitude but acting in opposite direction is

called couple c. One force acting in a fixed member will cause moment d. One force acting in a fixed member will cause couple e. One force acting in a member will cause moment f. One force acting in a member will cause couple

Correct Response: a, c Distractor 1: b, c Distractor 2: a, b Distractor 3: e, f Distractor 4: c, e Distractor 5: none of the options

4. Identify the wrong statement among the following with respect to the hinged support

a. simplest type of support b. also called as pin joint c. resist only displacement d. horizontal force is zero

Correct Response: only a Distractor 1: only b Distractor 2: only c Distractor 3: only d Distractor 4: a, c Distractor 5: none of the options

5. Identify the true statement among the following with respect to the supports in beam

a. roller support has known line of action of reaction b. hinged support has an unknown line of action of reaction c. fixed support is the strongest of all the support d. roller support is the simplest support

Correct Response: all the options Distractor 1: none of the options Distractor 2: a, b and c

Distractor 3: a, b and d Distractor 4: a, c Distractor 5: b, c

6. Determine the moment of force F1 about point A on the beam.

Correct Response: M1 = 1600 ft-lb

Distractor 1: M1 = 1600 ft-lb





7. The boys A, B and C stand near the edges of a raft as shown. Determine the location (x, y) of boy D so that all four boys create a single resultant force acting through the raft's centre O. Provided the raft itself is symmetric, this would keep the raft afloat in a horizontal plane. The mass of each boy is indicated in the diagram.

Correct Response: x = 1.5 m, y = 4.5 m Distractor 1: x = 4.5 m, y = 1.5 m Distractor 2: x = 3.0 m, y = 3.0 m Distractor 3: x = 3.0 m, y = 4.0 m Distractor 4: x = 4.0 m, y = 1.5 m Distractor 5: x = 4.0 m, y = 1.0 m

8. A force of 50 N is applied to the handle of the door as shown. Determine the projection of the moment of this force about the hinged axis z. Neglect the size of the doorknob

Correct Response: Mz = -15.9 N-m Distractor 1: Mz = 15.9 N-m Distractor 2: Mz = -27.6 N-m Distractor 3: Mz = 27.6 N-m Distractor 4: Mz = -13.9 N-m Distractor 5: Mz = 13.9 N-m

9. Determine the direction (0 180) of the 30-lb force F so that the moment of F about point A has the maximum magnitude.

Correct Response: = 36.9 Distractor 1: = 53.1 Distractor 2: = 127.0 Distractor 3: = 90.0 Distractor 4: = 45.0

Distractor 5: = 135.0

10. According to the principle of moments, which of the following statement are correct

Correct Response: = if a system of coplanar forces is in equilibrium, then their algebraic sum is zero

Distractor 1: = if a system of coplanar forces is in equilibrium, then their algebraic sum is not zero Distractor 2: = if a system of coplanar forces is in equilibrium, then their algebraic sum of their moments about any point in their plane is zero Distractor 3: = if a system of coplanar forces is in equilibrium, then their algebraic sum of their moments about any point in their plane is not zero Distractor 4: = the algebraic sum of the moments of any two forces about any point is equal to moment of their resultant about the same point Distractor 5: = the algebraic sum of the moments of any two forces about any point is not equal to moment of their resultant about the same point

11. Couple is defined as

Correct Response: = 2 forces, equal magnitude, opposite sensed parallel forces, lie in same plane Distractor 1: = 2 forces, unequal magnitude, opposite sensed parallel forces, lie in same plane Distractor 2: = 3 forces, equal magnitude, opposite sensed parallel forces, lie in same plane Distractor 3: = 2 forces, equal magnitude, opposite sensed parallel forces, lie in same plane Distractor 4: = None of the options Distractor 5: = A moment is necessary to produce a couple

12. Varignon's theorem of moments states that if a number of coplanar forces acting on a particle are in equilibrium, then

Correct Response: the algebraic sum of their moments about any point is equal to the moment of their resultant force about the same point. Distractor 1: their lines of action are at equal distances Distractor 2: their algebraic sum is zero Distractor 3: the algebraic sum of their moments about any point in their plane is zero Distractor 4: None of the options Distractor 5: the algebraic sum of their moments about any plane in their plane is zero

13. A couple produces

Correct Response: rotational motion Distractor 1: translatory motion Distractor 2: combined translatory and rotational motion Distractor 3: Linear motion Distractor 4: None of the options Distractor 5: Does not produce motion at all

14. The moment of a force

Correct Response: All of the options Distractor 1: is the turning effect produced by a force, on the body, on which it acts Distractor 2: is equal to the product of force acting on the body and the perpendicular distance of a point and the line of action of the force Distractor 3: is equal to twice the area of the triangle, whose base is the line representing the force and whose vertex is the point, about which the moment is taken Distractor 4: None of the options Distractor 5: Is produced in a cantilever beam

15. According to the law of moments, if a number of coplanar forces acting on a particle are in equilibrium, then

Correct Response: the algebraic sum of their moments about any point in their plane is zero Distractor 1: their lines of action are at equal distances Distractor 2: the algebraic sum of their moments about any point is equal to the moment of their resultant force about the same point. Distractor 3: their algebraic sum is zero Distractor 4: None of the options Distractor 5: All of the options

16. The algebraic sum of moments of the two parallel forces with respect to any moments centre in their plane of action is equal to the moment of their resultant with respect to the same centre. This statement is known as

Correct Response: Varignons theorem Distractor 1: Superposition theorem Distractor 2: theorem of transmissibility of forces. Distractor 3: Lami's theorem Distractor 4: None of the options Distractor 5: Equilibrium Law

17. Reactions equivalent to a force and a couple are the reactions caused by _______

Correct Response: fixed supports Distractor 1: hinged supports Distractor 2: 2 roller supports Distractor 3: 3 roller supports Distractor 4: cantilever supports Distractor 5: none of the options

18. The number of supports in a frictionless pin is

Correct Response: 2 Distractor 1: 3 Distractor 2: 1 Distractor 3: 4

Distractor 4: there is nothing like a frictionless pin Distractor 5: none of the options

19. A force produces __________ moment about an axis or reference point which intersects the line of action of the force.

Correct Response: 0 Distractor 1: depends upon the magnitude of the force Distractor 2: depends upon the direction of the force Distractor 3: depends upon the direction and the magnitude of the force Distractor 4: depends upon the position of the force in the member Distractor 5: none of the options

20. Point loads are otherwise called as ___________

Correct Response: concentrated load Distractor 1: Uniformly distributed load Distractor 2: Uniformly varying load Distractor 3: hinged load Distractor 4: all the options Distractor 5: none of the options

21. A couple is completely defined by its

I. plane of action II. Magnitude

III. Sign of its moment

Correct Response: all options are true Distractor 1: only I is true Distractor 2: only III is true Distractor 3: only II is true Distractor 4: both I and II are true Distractor 5: both I and III are true

22. Consider the following statements regarding the properties of couple.

I. the algebraic sum of the moments of the two forces of a couple is independent of the position in the plane of the couple of the moment centre and is always equal to the product of the magnitude of either force and the arm of the couple.

II. We can transpose a couple in its plane without changing its action on a body

III. Two couples acting in the same plane are equivalent if they have equal moments.

Correct Response: all options are true Distractor 1: only I is true Distractor 2: only III is true Distractor 3: only II is true

Distractor 4: both I and II are true Distractor 5: both I and III are true

23. Which of the following system is not equivalent to the couple in

Correct Response:

Distractor 1:

Distractor 2:

Distractor 3: Distractor 4: the given data is insufficient to solve the problem Distractor 5: none of the options

24. The force of 200N acting on the lever can be replaced by which of the following?

Correct Response: A force of 400 N at O and a couple of 69.3 Nm at O Distractor 1: A force of 400 N at O Distractor 2: A couple of 69.3 Nm at O Distractor 3: A couple of 100 Nm at O Distractor 4: All of the options Distractor 5: None of the options

25. The moment of inertia of an area is

Correct Response: 4 Distractor 1: 2

Distractor 2:

2

Distractor 3:

Distractor 4:

3

Distractor 5: None of the options

26. A twist of 4 N-m is applied to the handle of the screwdriver. Resolve this couple moment into a pair of couple forces F exerted on the handle.

Correct Response: 133N Distractor 1: 120N Distractor 2: 60N Distractor 3: 66N Distractor 4: 266N Distractor 5: 166N

27. The three forces acting on the water tank represent the effect of the wind. Replace this system by a single resultant force and specify its vertical location from point O.

Correct Response: R = 600 lb, d = 130.4 ft above O Distractor 1: R = 600 lb, d = 65.0 ft below O Distractor 2: R = 600 lb, d = 130.4 ft below O Distractor 3: R = 600 lb, d = 65.0 ft above O Distractor 4: R = 600 lb, d = 75.0 ft above O Distractor 5: none of the options

28. Determine the magnitude and direction of the moment of the force at A about point P.

Correct Response: Mp = 1104 ft-lb

Distractor 1: Mp = 143.5 ft-lb

Distractor 2: Mp = 1191 ft-lb




29. Which of the following do not have identical dimensions?

Correct Response: Moment of a force and angular momentum. Distractor 1: Momentum and impulse Distractor 2: Torque and energy Distractor 3: Torque and work Distractor 4: Kinetic energy and potential energy Distractor 5: None of the options

30. If a number of forces act simultaneously on a particle, it is possible

Correct Response: to replace them by a single force Distractor 1: not a replace them by a single force Distractor 2: to replace them by a single force through C.G. Distractor 3: to replace them by a couple Distractor 4: to replace them by a couple and a force. Distractor 5: None of the options Third Unit

1. Determine the approximate amount of paint needed to cover the surface of the water storage tank. Assume that a litter of paint covers 2.5. Also, what is the total inside volume of the tank?

Correct Response: 26.4 litters of paint, V = 56.53. Distractor 1: 27.4 litters of paint, V = 56.5 3 Distractor 2: 20.4 litters of paint, V = 56.5 3 Distractor 3: 26.4 litters of paint, V = 50.5 3 Distractor 4: 20.4 litters of paint, V = 50.5 3 Distractor 5: 27.4 litters of paint, V = 50.5 3

2. Determine the distance y to the centroid axis xx of the beam's cross sectional area. Neglect the size of the corner welds at A and B for the calculation

Correct Response: y = 85.9 mm Distractor 1: y = 75.2 mm Distractor 2: y = 97.5 mm Distractor 3: y = 102.5 mm Distractor 4: y = 85.2 mm Distractor 5: y = 86.9 mm

3. Determine the volume of concrete needed to construct the circular curb

Correct Response: 1.083 3 Distractor 1: y = 1.309 3 Distractor 2: y = 1.756 3 Distractor 3: y = 8.67 3 Distractor 4: y = 1.409 3 Distractor 5: y =1.903 3

4. Determine the distance Y to the centroidal axis XX of the beam's cross-sectional area.

Correct Response: 91.7 mm Distractor 1: y = 112.3 mm Distractor 2: y = 125 mm Distractor 3: y = 100 mm Distractor 4: y = 92.7 mm Distractor 5: y = 92.9 mm

5. The truss is made from seven members, each having a mass of 6kg/m. Locate the centroidal position, neglecting the mass of the gusset plates at the joints

Correct Response: x = 2.43 mm, y = 1.308 mm Distractor 1: x = 2.36 mm, y = 1.286 mm Distractor 2: x = 2.33 mm, y = 1.333 mm Distractor 3: x = 2.79 mm, y = 1.757 mm Distractor 4: x = 3.79 mm, y = 1.757 mm Distractor 5: x = 2.79 mm, y = 2.757 mm

6. Determine the inertia of the parabolic area about the x axis

Correct Response: 11430 4 Distractor 1: 32800 4 Distractor 2: 13300 4 Distractor 3: 21300 4 Distractor 4: 22300 4 Distractor 5: 21000 4

7. Locate the centre of gravity of the volume generated by revolving the shaded area about the Z axis. The material may be considered as homogenous

Correct Response: 2.67 ft Distractor 1: 2.80 ft Distractor 2: 2.69 ft Distractor 3: 2.50 ft Distractor 4: 2.20 ft Distractor 5: none of the options

8. The figure refers to a channel section of uniform thickness of 1 cm used as a beam with the cross-sectional dimensions shown in the figure below. If the moment of inertia of the channel Ixx be equal to 246 4 and then the value of e is equal to

Correct Response: 1.5 Distractor 1: 2.5 Distractor 2: 3.5 Distractor 3: 2 Distractor 4: 3 Distractor 5: none of the options

9. Among the following statement identify the wrong statement

1. Weight acts through the centroid 2. Weight is the resultant force of all the small elements 3. Weight may not act at the centroid 4. Centroid may not be the geometric centre of the object

Correct Response: both 1 & 2 Distractor 1: both 2 & 3 Distractor 2: both 1 & 3 Distractor 3: 2 Distractor 4: 3 Distractor 5: none of the options

10. ____________ is defined as the point at which the total area of plane figures namely rectangle, triangle, circle etc. is assumed to be concentrated.

Correct Response: centroid Distractor 1: weight Distractor 2: centre of gravity Distractor 3: centre of buoyancy Distractor 4: concurrent point Distractor 5: none of the options

11. Area of curved region

Correct Response:

4

Distractor 1:

2

Distractor 2:

4

Distractor 3:

2

Distractor 4:

Distractor 5: none of the options

12. On a square of 6 X 6 cm dimensions, a triangle of base 5 cm and altitude 6 cm is placed. The centroid of composite sections lies at a distance of Y from the base of square. The value of Y is

Correct Response: 4.47 cm Distractor 1: 5 cm

Distractor 2: 4.33 cm Distractor 3: 4 cm Distractor 4: 3.47 cm Distractor 5: 5.47cm

13. The centroid of a semi-circular area of radius R lies at a distance of Y from the diameter. The value of Y


Distractor 1: 3

Distractor 2:

Distractor 3: 4

Distractor 4: 34


14. The ellipse has major axis a and minor axis b. The centroid of semi elliptical area lies at a distance of Y from major axis. The value of Y is

Correct Response: 3

Distractor 1:

Distractor 2: 23

Distractor 3: 32

Distractor 4: 34


15. Centre of gravity of a hemisphere lies at a distance of Y from the base. The value of Y is

Correct Response: 0.375 R Distractor 1: 0.5 R Distractor 2: 0.45 R Distractor 3: 0.55 R Distractor 4: 0.425 R Distractor 5: none of the options

16. An area is covered by a curve = 2 , x-axis and a vertical line x=a. Its centroid from y-axis lies at a distance of

Correct Response: 0.6 a Distractor 1: 0.65 a Distractor 2: 0.75 a Distractor 3: 0.5 a Distractor 4: 0.45 a Distractor 5: none of the options

17. An area is covered by a curve = 3 , passing through the origin and other end of curve has co-ordinate (a,b). Centroid of the covered area lies at a distance of Y from the x-axis. The value of Y is

Correct Response: 0.4 b Distractor 1: 0.75 b Distractor 2: 0.5 b Distractor 3: 0.4 b Distractor 4: 0.7 b Distractor 5: none of the options

18. For a rectangular wire ABCD. About which axis, the moment of inertia of the wire will be minimum? (given BC=2AB)

Correct Response: EG Distractor 1: BC Distractor 2: BD Distractor 3: HF Distractor 4: AC Distractor 5: none of the options

19. A thin uniform rod AB of mass 12m & length L has moment of inertia I about ab axis passing through its mid-point O perpendicular to its length. If a portion CB of length (L/4) is cut off from the end of the rod, the moment of inertia of the remaining portion AC about the original axis through O will be

Correct Response: 9

16

Distractor 1: 3

4

Distractor 2: 13

15

Distractor 3: 13

16

Distractor 4: 41

48

Distractor 5: 5

16

20. Identify the wrong statement among the following

1. the position of the centre of mass depends upon the shape of the body 2. if a body is symmetrical, then its centre of mass will coincide with the

symmetrical axis 3. the position of the centre of mass does not depend on the co-ordinate axis

position 4. there may or may not be any mass at the centre of mass

Correct Response: all the options Distractor 1: 1, 2 and 3 Distractor 2: 1, 2 and 4 Distractor 3: 2, 3 and 4

Distractor 4: both 1 and 2 Distractor 5: both 2 and 3

21. A certain coin and a wedding ring having exactly the same mass and radius, when placed at the top of an inclination which object will reach the bottom first

Correct Response: the coin Distractor 1: the wedding ring Distractor 2: both will reach at the same time Distractor 3: given data is not sufficient Distractor 4: both will stop at intermediate level Distractor 5: both will not start from the top, because of the resistive frictional force

22. An ice skater is in a fast spin with her arms held tightly to his/her body. When he/she extends her arms, which of the following statements in not true?

Correct Response: his/her moment of inertia remains constant Distractor 1: he/she increases his/her moment of inertia Distractor 2: he/she decreases her angular speed Distractor 3: his/her total angular momentum remains constant Distractor 4: he/she will fall after some time Distractor 5: none of the options

23. Among the figures that are presented above the centroidal axis is also shown. Identify the one which has the maximum moment of inertia

Correct Response: ring Distractor 1: cross Distractor 2: sphere Distractor 3: cube Distractor 4: rod Distractor 5: all will have same moment of inertia

24. To increase the moment of inertia of a body about an axis, which should be done among the following

Correct Response: the mass distribution Distractor 1: the angular velocity Distractor 2: the angular acceleration Distractor 3: the torque acting on the body Distractor 4: the linear acceleration Distractor 5: none of the options

25. A solid disk has a mass M and radius R. What is the moment of inertia along an axis which is perpendicular to the disk and passes through its edge?

Correct Response: 3

22

Distractor 1: 2

52

Distractor 2: 1

22

Distractor 3: 22 Distractor 4: 2 Distractor 5: none of the options

26. Two circular coins, each of mass M and radius R, are welded together at a point as shown. What is the moment of inertia of the pair about the axis perpendicular through their contact point

Correct Response: 32 Distractor 1: 22 Distractor 2: 2 Distractor 3: 42

Distractor 4: 3

22


27. Two coins area made from identically the same metal, but one coin has triple the diameter of the other. What is the ratio of the moment of inertia of the large coin compared to the small coin? Take the axis of rotation to be perpendicular to the coin and through its centre, assume that the coins have the same thickness

Correct Response: 81 Distractor 1: 243 Distractor 2: 27 Distractor 3: 9 Distractor 4:3 Distractor 5: none of the options

28. What is the moment of inertia of two objects of mass m separated by a rigid rod of length 2R, as in the diagram? Take the axis for the moment to intersect the rod at an angle 45

Correct Response: 2

Distractor 1: 4

32

Distractor 2: 1

32


29. Consider four objects arranged at the corners of a square having dimensions L*L. What is the moment of inertia of this configuration with respect to an axis lying in the plane of the objects? Each mass is equal to M and is concentrated at a point

Correct Response: 2

Distractor 1: 1

22

Distractor 2: 1

32


30. The moment of inertia depends upon

Correct Response: the mass distribution Distractor 1: the angular velocity Distractor 2: the angular acceleration Distractor 3: the torque acting on the body Distractor 4: the linear acceleration Distractor 5: none of the options

Fourth Unit

1. A two-stage missile is fired vertically from rest with an acceleration as shown in the graph. In 15 s the first stage A burns out and the second stage B ignites. How fast is the rocket moving and how far has it gone at t = 20 s? How fast is the missile moving and how far has it gone at t = 20 s?

Correct Response: v = 395 m/s, s = 3.69 km Distractor 1: v = 430 m/s, s = 4.30 km Distractor 2: v = 360 m/s, s = 3.60 km Distractor 3: v = 500 m/s, s = 5.00 km Distractor 4: v = 400 m/s, s = 5.00 km Distractor 5: v = 500 m/s, s = 4.00 km

2. A package is dropped from the plane which is flying with a constant horizontal velocity of vA = 150 ft/s at a height h = 1500 ft. Determine the radius of curvature of the path of the package just after it is released from plane at A.

Correct Response: 8510 ft Distractor 1: 9860 ft Distractor 2: 4000 ft Distractor 3: 5000 ft Distractor 4: 1500 ft Distractor 5: 2500 ft

3. The motorcyclist attempts to jump over a series of cars and trucks and lands smoothly on the other ramp, i.e., such that his velocity is tangent to the ramp at B. Determine the launch speed vA necessary to make the jump.

Correct Response: vA = 16.83 m/s Distractor 1: vA = 11.90 m/s Distractor 2: vA = 11.07 m/s Distractor 3: vA = 15.66 m/s Distractor 4: vA = 14.66 m/s Distractor 5: vA = 13.66 m/s

4. A United Airlines jet is flying at 300 km/hr, while an Air France Concord is speeding along at 1200 km/hr Both airplanes are flying at the same altitude If each aircraft experiences problems with an unruly passenger, and they both decide simultaneously to push the passenger out the door, which of the unruly passengers will hit the earth first? (Ignore air resistance)

Correct Response: both will reach the earth at the same time Distractor 1: Air France passenger Distractor 2: United Airlines Distractor 3: impossible to answer, the time duration is very small for any calculations to be made Distractor 4: impossible to answer, depends upon the weight of the passenger Distractor 5: none of the options

5. A United Airlines jet is flying at 300 km/hr, while an Air France Concord is speeding along at 1200 km/hr Both airplanes are flying at the same altitude If each aircraft experiences problems with an unruly passenger, and they both decide simultaneously to push the passenger out the door, they continue to travel at the same velocity after ejecting their respective passengers, where will the passengers land with respect to their aircraft's path? (Ignore air resistance)

Correct Response: When they hit the ground, they will be directly beneath the airplane they fell from Distractor 1: When they hit the ground, they will be directly beneath the spot at which the airplane threw them out Distractor 2: United Airlines Distractor 3: They will be in front of the aircraft they fell from Distractor 4: It depends upon the velocity of the aircraft Distractor 5: none of the options

6. A raindrop on a drizzly day takes one minute from the time it leaves the cloud until it hits your umbrella, 3 miles below The average velocity of the raindrop on its journey is

Correct Response: 180 miles/hr Distractor 1: 3 miles/hr Distractor 2: 60 miles/hr Distractor 3: Impossible to determine because the raindrop accelerates due to gravity Distractor 4: 20 miles/hr Distractor 5: none of the options

7. The average velocity and the instantaneous velocity of an object will be the same if

Correct Response: the object acceleration is zero Distractor 1: the object's speed is constant the object's speed is constant Distractor 2: they will never be the same Distractor 3: the object's velocity is always positive Distractor 4: the object has constant acceleration Distractor 5: none of the options

8. A car traveling at constant velocity v suddenly brakes in an effort to keep from hitting a rabbit which is 8 ft away if the braking action causes a constant deceleration a, how long does it take for the car to come to a complete stop?

Correct Response: =

Distractor 1: = Distractor 2: = 8

Distractor 3: =8

Distractor 4: =


9. Phin and Wittgenstein are hanging out on the moon when they decide to have a contest to see who can shoot a bullet farther both use identical guns Phin decides to shoot at a 60 degree angle, while Wittgenstein holds his gun at 45 degrees when shooting whose bullet lands the furthest away?

Correct Response: Wittgenstein's Distractor 1: Phin's Distractor 2: Both bullets land the same distance away Distractor 3: Impossible to determine without knowing the acceleration due to gravity on the moon Distractor 4: Since the gravity is less the path can't be defined Distractor 5: none of the options

10. What does the above s-t graph represent

Correct Response: body is at rest Distractor 1: uniform acceleration Distractor 2: uniform velocity Distractor 3: variable acceleration

Distractor 4: variable velocity Distractor 5: none of the options

11. A ball initially at rest t = 0 seconds, rolls down a long incline. Since the object is on the incline, its acceleration will be less than 9.8 m/s2 although the acceleration will still be constant. If the ball has rolled 1 meter at t = 2 seconds, how far will it have rolled at t = 4 seconds

Correct Response: 4 m Distractor 1: 2 m Distractor 2: 3 m Distractor 3: 5 m Distractor 4: 8 m Distractor 5: none of the options

12. Each of the three graphs above represent acceleration versus time for an object that already has a non-zero positive velocity at time t1. Which graphs show an object whose speed is increasing for the entire time interval between t1 and t2

Correct Response: all the graphs Distractor 1: graph I only Distractor 2: graph II only Distractor 3: graph III only Distractor 4: graph I and II only Distractor 5: graph I and III only

13. Two balls have been dropped, at slightly different times, from the top of very tall office building. At a certain time the difference between their speeds is 4.0 m/s. What is the difference between their speeds two seconds later

Correct Response: 4 m/s Distractor 1: 24 m/s Distractor 2: 16m/s Distractor 3: 20 m/s Distractor 4: 44 m/s Distractor 5: none of the options

14. The speed of an object one second after it has been dropped from rest out of high office window on a planet is 8 m/s. What will its speed be 3 seconds after it was first dropped.

Correct Response: 24 m/s Distractor 1: 24 m/s Distractor 2: 16m/s Distractor 3: 20 m/s Distractor 4: 44 m/s Distractor 5: none of the options

15. The limiting friction is

Correct Response: always greater than the dynamic friction Distractor 1: equal to the dynamic friction Distractor 2: always less than the dynamic friction Distractor 3: sometimes greater and sometimes lesser than the dynamic friction Distractor 4: always greater than the kinematic friction Distractor 5: equal to kinematic friction

16. When a body is moving on a surface, the force of friction is called as

Correct Response: dynamic friction Distractor 1: static friction Distractor 2: limiting friction Distractor 3: rolling friction Distractor 4: kinetic friction Distractor 5: none of the options

17. A force of 98 N is required to just start moving a body of mass 100 kg over ice. The co-efficient of static friction is

Correct Response: 0.1 Distractor 1: 0.2 Distractor 2: 0.3 Distractor 3: 0.4 Distractor 4: 0.5 Distractor 5: 0.6

18. Two carts of masses 200 kg and 300 kg on horizontal rails are pushed apart. Suppose the coefficient of friction between the carts and the rails are same. If the 200 kg cart travels a distance of 36 m and stops, then the distance travelled by the cart weighing 300 kg is

Correct Response: 16 m Distractor 1: 24 m Distractor 2: 34 m Distractor 3: 20 m Distractor 4: 46 m Distractor 5: 50 m

19. To avoid slipping while walking on ice, one should take smaller steps because of the

Correct Response: friction of ice is small Distractor 1: friction of ice is large Distractor 2: larger normal reaction Distractor 3: smaller normal reaction Distractor 4: none of the options Distractor 5: the given data is not sufficient

20. A body B lies on a smooth horizontal table and another body A is placed on B. The coefficient of friction between A and B is . What acceleration given to B will cause slipping to occur between A and B

Correct Response:

Distractor 1:

Distractor 2:

Distractor 3:

Distractor 4:

Distractor 5:

21. A heavy uniform chain lies on a horizontal table top. If the coefficient of friction between the chain and table surface is 0.25, then the maximum fraction of length of the chain, that can hang over one edge of the table is

Correct Response: 20 % Distractor 1: 25 % Distractor 2: 30 % Distractor 3: 35 % Distractor 4: none of the options Distractor 5: 15 %

22. Assuming the coefficient of friction between the road and tyres of a car to be 0.5, the maximum speed with which the car can move round a curve of 40.0 m radius without slipping, if road is unbanked, should be

Correct Response: 14 m/s Distractor 1: 25 m/s Distractor 2: 30 m/s Distractor 3: 35 m/s Distractor 4: none of the options Distractor 5: 15 m/s

23. When a body is lying on a rough inclined plane and does not move, the force of friction

Correct Response: lesser than Distractor 1: greater than Distractor 2: equal to Distractor 3: equal to R Distractor 4: greater than R Distractor 5: lesser than R

24. A block weighs W is held against a vertical wall by applying a horizontal force F. The minimum value of F needed to hold the block is

Correct Response: greater than W Distractor 1: lesser than W Distractor 2: equal to W Distractor 3: data is insufficient Distractor 4: none of the options Distractor 5: friction will be the deciding factor

25. A 20 kg block is initially at rest on a rough horizontal surface. A horizontal surface of 75 N is required to set the block in motion. After it is in motion, a horizontal force of 60 N is required to keep the block moving with constant speed. The coefficient of static friction is

Correct Response: 0.38 Distractor 1: 0.28 Distractor 2: 0.24 Distractor 3: 0.5 Distractor 4: none of the options Distractor 5: 0.48

26. The coefficient of friction and the angle of friction are related as

Correct Response: = Distractor 1: = Distractor 2: = Distractor 3: = Distractor 4: = Distractor 5: =

27. The maximum static frictional force is

Correct Response: independent of the area of surface on contact Distractor 1: equal to twice the area of surface in contact Distractor 2: equal to the area of surface on contact Distractor 3: 0.5 Distractor 4: equal to thrice the area of surface on contact Distractor 5: equal to half of area of surface in contact

28. A horizontal force of 10 N is necessary to just hold a block of stationary against a wall. The coefficient of friction between the block and the wall is 0.2, the weight of the block is

Correct Response: 2 N Distractor 1: 50 N Distractor 2: 25 N Distractor 3: 20 N Distractor 4: 100 N Distractor 5: none of the options

29. Which pair of graphs shows the distance travelled versus time and the speed versus time for an object uniformly accelerated from rest starting at time t =0

Correct Response:

Distractor 1:

Distractor 2:

Distractor 3:

Distractor 4:


30. Two astronauts are attempting to measure g, the acceleration due to gravity, on a new planet they have discovered. One astronaut drops a ball while the other one times the fall. It turns out that the ball falls through a distance s in a time interval t.

Neglecting air friction, which of the following expressions for the acceleration due to gravity on this planet is correct?

Correct Response: =2

2

Distractor 1: =

Distractor 2: = 2

Distractor 3: =

2

Distractor 4: = 2

2

Distractor 5: none of the options Fifth unit

1. Two balls of equal mass and of perfectly elastic material are lying on the floor. One of the ball with velocity v is made to strike the second ball. Both the balls after impact will move with a velocity

Correct Response: v/2 Distractor 1: v Distractor 2: v/4 Distractor 3: v/8 Distractor 4: 2v Distractor 5: 4v

2. During elastic impact, the relative velocity of the two bodies after impact is _______ the relative velocity of the two bodies

Correct Response: equal and opposite to Distractor 1: equal to Distractor 2: 1/3 than Distractor 3: 1/4 than Distractor 4: twice Distractor 5: thrice

3. Work done is said to be zero, when

1. some force acts on a body and displacement is small 2. some force acts on a body and displacement is zero 3. no force acts on a body but some displacement takes place

Correct Response: 2, 3 Distractor 1: 1, 2 Distractor 2: only 1 Distractor 3: only 2

Distractor 4: only 3 Distractor 5: none of the options

4. If 1 and 2 are the velocities of two moving bodies in the same direction before impact and 1 and 2 are their velocities after impact, then the coefficient of restitution is


12

Distractor 1: 2+1

12

Distractor 2: 21

1+2

Distractor 3: 2+1

1+2

Distractor 4: 21

21

Distractor 5: 21

2+1

5. In the shown figure, the tension (T) in the string will be


1+2

Distractor 1: 12

1+2

Distractor 2: 1+2

12

Distractor 3: 12

12

Distractor 4: they cant be related Distractor 5: none of the options

6. Two bodies of masses 1 and 2 are hung from the ends of a rope, passing over a frictionless pulley as in figure, The acceleration of the string will be

Correct Response: (12)

1+2

Distractor 1: (1+2)

1+2

Distractor 2: (12)

12

Distractor 3: (21)

1+2

Distractor 4: (12)

(1+2)

Distractor 5: (1+2)

(1+2)

7. When a force acts on a body and then it undergoes a displacement, then

Correct Response: a work is said to be done Distractor 1: a deformation is said to be done Distractor 2: power is produced by the body Distractor 3: the body will have uniform acceleration Distractor 4: the body will have uniform velocity Distractor 5: none of the options

8. If the tension in the cable supporting a lift moving downwards is half the tension when it is moving upwards, the acceleration of the lift is

Correct Response: none of the options

Distractor 1:

2

Distractor 2:

3

Distractor 3:

4

Distractor 4: 2 Distractor 5: 4

9. When two elastic bodies collide with each other, then

1. two bodies will momentarily come to rest after collision 2. two bodies tend to compress and deform at the surface of contact 3. two bodies begin to regain their original shape 4. two bodies will undergo deformation momentarily

Correct Response: all the options Distractor 1: only 1 Distractor 2: only 2 Distractor 3: only 3 Distractor 4: both 1 and 3 Distractor 5: both 2 and 3

10. A body of mass m moving with a constant velocity v strikes another body of same mass m moving with same velocity but in opposite direction. The common velocity of both the bodies after the collision is

Correct Response: 2v Distractor 1: v Distractor 2: 3v Distractor 3: 4v Distractor 4: 8v Distractor 5: 6v

11. A lead ball with a certain velocity is made to strike a wall, it falls down, but the rubber ball of same mass m and with same velocity strikes the same wall and rebounds. Select the correct reason from the following:

Correct Response: the change in the momentum suffered by the rubber ball is more than the lead ball Distractor 1: both the balls undergo an equal change in momentum Distractor 2: the change in momentum suffered by rubber ball is less than the lead ball Distractor 3: the change in energy suffered by the rubber ball is more than the lead ball Distractor 4: the change in energy suffered by the rubber ball is less than the lead ball Distractor 5: none of the options

12. The velocity of a body on reaching the ground from a height h, is

Correct Response: 2

Distractor 1: 2

Distractor 2: 2

Distractor 3: 2

Distractor 4: Distractor 5: none of the options

13. The coefficient of restitution for inelastic bodies is

Correct Response: zero Distractor 1: one Distractor 2: half Distractor 3: one third Distractor 4: twice Distractor 5: thrice

14. An air glider of mass M is built consisting of two smaller connected gliders with a small explosive charge located between them. The glider is travelling along a frictionless rail at 2m/s to the right when the charge is detonated, causing the smaller glider with mass M/4, to move off to the right at 5m/s. What is the final velocity of the second small glider?

Correct Response: 1m/s to the right Distractor 1: 1m/s to the left Distractor 2: 4m/s to the left Distractor 3: 4m/s to the right Distractor 4: 2m/s to the left Distractor 5: 2m/s to the right

15. A student with mass M is standing on a wooden plank of mass m that is less than the mass of the student. The plank itself is resting on the frictionless surface of a frozen lake, the student then begins to walk with a speed v towards the nearby shore. What is the velocity of the plank relative to the shore

Correct Response: more than v, away from the shore Distractor 1: v, away from the shore Distractor 2: less than v, away from the shore Distractor 3: less than v, towards the shore Distractor 4: v, towards the shore Distractor 5: more than v, towards the shore

16. A boy on a sled is sliding with negligible friction along an icy, horizontal surface. As the sled passes underneath a tree, a large mass of snow falls vertically and lands on the moving sled. Which of the following statements is false

Correct Response: conservation of linear momentum cannot be used to find the final velocity of the sled Distractor 1: conservation of mechanical energy cannot be used to find the final velocity of the sled Distractor 2: conservation of kinetic energy cannot be used to find the velocity of the sled Distractor 3: the sled will slow down when the snow hits it Distractor 4: the snow collides in elastically with the sled Distractor 5: none of the options

17. A 500g cart rolls with negligible friction along a straight flat track until it collides with a 750g cart that was initially at rest. Position-time data for the 500g cart before it hits the other cart is recorded in the data table

Correct Response: 0.08 m/s to the right

Distractor 1: 0.08 m/s to the left Distractor 2: 8m/s to the right Distractor 3: 8m/s to the left Distractor 4: 10m/s to the left Distractor 5: 10m/s to the right

18. A pendulum of length L = 1m and bob with mass m = 1kg is released from the rest at an angle=30 from the vertical. When the pendulum reaches the vertical position the bob strikes a mass M = 3kg that is resting on a frictionless table that has a height h = 0.85m, when the pendulum reaches the vertical positon, calculate the speed of the bob just before it strikes the box.

Correct Response: 1.62m/s Distractor 1: 2.62m/s Distractor 2: 4.62m/s Distractor 3: 3.62m/s Distractor 4: 4.9m/s Distractor 5: none of the options


Correct Response: =0.81 /; = 0.81 /

Distractor 1: = 0.81 /; = 0.81 /

Distractor 2: =0.81 /; = 0.81 /

Distractor 3: =0.81 /; = 0.81 /

Distractor 4: =1.81 /; = 0.81 /



Correct Response: 2.43kgm/s Distractor 1: 1.43kgm/s Distractor 2: 0.43kgm/s Distractor 3: 4.43kgm/s Distractor 4: 5.43kgm/s Distractor 5: none of the options

21. A lump of clay (1 = 0.2) moving horizontally with a speed 01= 16 m/s strikes and sticks to a wood block (2 = 3) which is initially at rest on the edge of a horizantal table of height h = 1.5m. Neglecting the friction find the final velocity of the combined wood and clay

Correct Response: 1 m/s Distractor 1: 2 m/s Distractor 2: 3 m/s Distractor 3: 4.43 m/s Distractor 4: 5.43 m/s Distractor 5: the data is not sufficient

22. In case of motion of two bodies (1 > 2) connected over rough inclined planes, the tension (T) in the string is given by


1+21 + 2

Distractor 1: 212

1+21 + 2

Distractor 2: 12

1+21 2

Distractor 3: 212

1+21 2

Distractor 4: 12

1+21 + 22

Distractor 5: 12

1+21 22

23. In case of motion of two bodies (1 > 2) connected by a string one end of which is hanging free and the other lying on a smooth inclined plane, the tension (T) in the string is given by

Correct Response: 12(1+)

1+2

Distractor 1: 12(1+)

21+2

Distractor 2: 12(1)

21+2

Distractor 3: 12(1)

1+2


1+2

Distractor 5: 212(1)

1+2

24. In case of motion of two bodies (1 > 2) connected at the edge of a rough horizontal surface of coefficient of friction the tension on the string is

Correct Response: 12(1+)

1+2

Distractor 1: 12(1)

1+2


2(1+2)

Distractor 3: 12(1)

2(1+2)


1+2

Distractor 5: 212(1)

1+2

25. An athlete runs some distance before taking a long jump because

Correct Response: by running the athlete gives himself larger moment of inertia Distractor 1: he gains energy to take him through long distance Distractor 2: it helps him to apply large force Distractor 3: by running action and reaction forces increase Distractor 4: data is not sufficient Distractor 5: data is not sufficient

26. A driver accelerates his car first at the rate of 1.8/2 and then at the rate of 1.2/2. The ratio of the two forces exerted by the engine in two cases will be

Correct Response: 2:3

Distractor 1: 3:2 Distractor 2: 1:2 Distractor 3: 1:3 Distractor 4: 3:4 Distractor 5: 1:4

27. Newton's law of motion gives the measure of

Correct Response: force Distractor 1: inertia Distractor 2: acceleration Distractor 3: momentum Distractor 4: impulse Distractor 5: speed

28. /2 is a unit of:


29. Rate of change of momentum is equal to


30. When a net force acts on an object, the object will be accelerated in the direction of force with acceleration proportional to

Correct Response: force on the object Distractor 1: velocity of the object Distractor 2: mass of the object Distractor 3: inertia of the object Distractor 4: none of the option Distractor 5: momentum of the object

Offline Questions

First Unit

1. Determine the force F needed to hold the 4kg lamp in the position shown

2. Determine the force in each strut and tell whether it is in tension or compression.

3. The patella P located in the human knee joint is subjected to tendon forces T1 and T2 and a force exerted on the patella by the femoral articular. If the directions of these forces are estimated from an X-ray as shown, determine the magnitude of T1 and F when the tendon force T2 = 6lb. The forces are concurrent at point O. (proceed the problem without changing the units)

4. The ends of the three cables are attached to ring at A and to the edge of a uniform 150-kg plate. Determine the tension in each of the cables for equilibrium.

5. Determine the magnitude and direction of the resultant force FAB exerted along link AB by the tractive apparatus shown. The suspended mass is 10 kg. Neglect the size of the pulley at A.

Second Unit

1. (a) Calculate the reaction forces that are present in the support, in the following figure

(b) A uniform plate grider of mass 250 kg is held in horizontal position by two cables attached at A & B as shown the following figure. Determine the angle alpha and the tension in each side

2. Find the reactions that are present in the support shown in the above figure.

3. (a) Find the reaction force that are present in the support, for the following figure as shown below,

(b) Find the reaction force that are present in the support, for the following figure as shown below,

4. Find the reaction force present at the support for the following figure

5. (a) Find the reaction at the support for the following figure

(b) Find the reaction at the support for the following figure

Third Unit:

1. Determine the centroid for the following images

2. Determine the position of the centroid for the following figure

3. (a) Determine the centroidal axis for the following figure

(b) A tank has a semi spherical dome at the left end. Using the theorems of Pappus and Giuldinus, compute the surface area and the volume of the tank

4. Find the moment of inertia for the following figure about the axis x,y which has the origin A

5. A beam cross-section is made up of an I shaped section with an additional thick plate welded to it. Find the second moment of area for the centroidal axes of the beam section

Fourth Unit

1. (a) An object is launched at 19.6 meters per second, from a 58.8 m tall platform. The equation for the object's height s at time t seconds after launch is =4.92 + 19.6 + 58.8, where s in meters. When does the object strike the ground? (b) In the given picture the motion path of cannonball is presented. Find the maximum height it can reach, horizontal distance it covers and total time from the given information. The angle between cannonball and horizontal is 53

2. (a) Two trains start a distance of 2000m apart. Train one is moving with a constant

speed of 30m/s directly towards train 2 which starts from rest and accelerates with a constant acceleration of 5 m/s directly towards train 1. When do the trains meet? (b) An airplane must reach a take-off speed of 80m/s in a 1000m long runway. What minimum acceleration is required for it?

3. A ball is launched from the ground with an initial speed of 40m/s at an angle of 45 above the horizontal towards a tall wall that is a horizontal distance of 100m from the launch point.

a. Where does the ball strike the wall? b. What are the ball's velocity components when it strikes the wall c. What is the speed of the ball when it strikes the wall?

4. Two sleds are tied together with a rope. The coefficient of static friction between each sled and the snow is 0.22. A small child is sitting on sled 1 (total mass of 27kg) and the larger child sits on sled 2 (total mass of 38 kg). An adult pulls on the sleds

a. What is the greatest horizontal force that the adult can exert on sled 1, without moving either sled

b. Calculate the magnitude of the tension in the rope between sled 1 and 2 when the adult exerts this greatest horizontal force.

5. Two trunks sit side by side on the floor. The larger trunk (52kg) is to the left of the smaller trunk (34kg). A person pushes on the larger trunk horizontally towards the right. The coefficient of static friction between the trunks and the floor is 0.35

a. Find the magnitude of the maximum force the person can exert without moving either trunk

b. Calculate the force the larger trunk exerts on the smaller trunk c. Would either answer change if the person pushed in the opposite direction

on the smaller trunk? Explain your answer with sufficient reason

Fifth Unit

1. Blocks A and B weighing 10N and 4N respectively are connected by a weightless rope passing over a frictionless pulley and are placed on smooth inclined planes 60 and 45 with the horizontal as in figure, determine

a. The tension in the string b. Velocity of the system 3 seconds after starting from rest

2. Determine the resulting motion of the body '1' assuming the pulleys to be smooth and weightless as in figure. If the system starts from rest, determine the velocity of the bodies after 5 seconds

3. A bullet weighing 30g moving with a velocity of 100m/s hits a 5kg bob of a simple pendulum horizontally. Determine the maximum angle through which the pendulum string 0.5m long may swing if

a. The bullet gets embedded in bob b. The bullet escapes from the other end at 20m/s c. The bullet is rebounded from the surface of the bob at 20m/s

4. A ball is dropped from a height of 6m upon a 25 incline. Find the resultant velocity of the ball after impact, if e = 0.8

5. A 40N ball traverse a frictionless tube as shown in the figure and falls through a height of 4m. It then strikes a 20N ball hung from a rope, 1.5m long. Determine the height to which the hanging ball will rise

a. If collision is perfectly elastic b. If the coefficient of restitution is 0.7

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Engineering Mechanics_course File