cjc JC1 Promo 2008 Answers

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CATHOLIC JUNIOR COLLEGE JC1 PROMOTIONAL EXAMINATION 2008

0800 – 1100 hrs

PHYSICS 9745 Higher 2

Thursday 2nd October 2008 3 hours

Additional materials: MCQ answer sheet for Section A Writing paper for Section B

READ THESE INSTRUCTIONS FIRST

There are 20 questions in Section A . Answer all questions.

Record your answer in soft 2B pencil on the MCQ answer sheet.

Each correct answer will score two marks. Marks will not be deducted for a wrong

answer.

Any rough working should be done in this booklet.

There are 9 questions in Section B . Answer all questions.

Begin each new question on a fresh sheet of writing paper.

Write in dark blue or black pen on the writing paper provided. You may use a soft

pencil for any diagrams, graphs or rough working.

The number of marks is given in brackets [ ] at the end of each question or part

question.

Total marks for Section B is 100 marks.

Do not use staples, paper clips, highlighters, glue or correction fluid.

Write your name and tutorial group on all the work you hand in.

Total marks for Section A and B is 140 marks.

A maximum of 2 marks will be deducted for mistakes made in units and

significant figures.

This question paper consists of 17 printed pages

2

© Catholic Junior College 9745/08 [TURN OVER]

PHYSICS DATA: speed of light in free space c = 3.00 x 108 m s-1

permeability of free space µo = 4π x 10-7 Hm-1

permittivity of free space εo = 8.85 x 10-12 F m-1

= (1/(36π )) x10-9 Fm-1

elementary charge e = 1.6 x 10-19 C

Planck constant h = 6.63 x 10-34 J s

unified atomic mass constant u = 1.66 x 10-27 kg

rest mass of electron me = 9.11 x 10-31 kg

rest mass of proton mp = 1.67 x 10-27 kg

molar gas constant R = 8.31 J K-1 mol-1

the Avogadro constant NA = 6.02 x 1023 mol-1

the Boltzmann constant k = 1.38 x 10-23 J K-1

gravitational constant, G = 6.67 x 10-11 N m2 kg-2

acceleration of free fall, g = 9.81 m s-2

3


PHYSICS FORMULAE : uniformly accelerated motion, s = u t + ½ a t2

v2 = u2 + 2 a s

work done on / by a gas, W = p ∆V

hydrostatic pressure P = ρgh

gravitational potential, φ =

r

Gm−

displacement of particle in s.h.m. x = x0 sin ωt

velocity of particle in s.h.m. v = v0 cos ωt

= 22

0 xx −ω±

resistors in parallel 1/Reff = 1 / R1 + 1 / R2 +…

resistors in series Reff = R1 + R2 +…

electric potential V =

r4Q

0πε

alternating current/voltage x = x0 sin ωt

transmission coefficient T = exp(-2kd)

where k =

2

2 )(8

h

EUm −π

radioactive decay x = )exp(0 tx λ−

decay constant λ =

2

1

693.0

t

4


SECTION A: MULTIPLE CHOICE QUESTIONS

1 The Stefan-Boltzmann law states that R, the total energy radiated by a blackbody per unit surface area

per unit time is given by R = σT4, where σ is the Stefan-Boltzmann constant, and T is the

thermodynamic temperature of the blackbody. What is the base unit of σ?

A kg s-3 K-4 B kg s-3 K4 C kg m2 s-2 K-4 D kg m2 s-2 K4

[ ] [ ][ ] [ ]

4-3-4

2

22

44

4

K s kg==

==

=−

K

sm

smkg

T

At

E

T

R

TR

σ

σ

2 Four students A to D measured and calculated the electronic charge, e. The table shows the results

obtained. Which student obtained a set of results that could be described as accurate but not precise?

Student Electron charge, e / 10-19 C

A 1.62 1.59 1.59 1.61 1.60

B 1.57 1.63 1.64 1.58 1.59

C 1.59 1.60 1.58 1.57 1.57

D 1.58 1.62 1.65 1.59 1.66

Student Electron charge, e / 10-19 C Average / 10-19 C

Conclusion

A 1.62 1.59 1.59 1.61 1.60 1.60 P, A B 1.57 1.63 1.64 1.58 1.59 1.60 NP, A C 1.59 1.60 1.58 1.57 1.57 1.58 P, NA D 1.58 1.62 1.65 1.59 1.66 1.62 NP, NA

3 A ball rolls off the top of a flight of steps. Assuming elastic collisions with the steps, which graph

shows the variation of the resultant vertical force, F acting on it with respect to time, t?

F A

t

F B

t

F C

t

F D

t

5


4 A particle starts from rest and moves in a straight line. Its motion is represented by the displacement–

time graph shown below. At which point is its velocity maximum?

Gradient of d-t graph is velocity, and gradient at point B is the steepest.

5 A cube of side length 0.100 m and mass 0.150 kg is held at the bottom of a pool of water. When

released, it rises up. Find the value of the drag force in Newton (N) due to water when it is travelling

with constant speed if the density of the water is 1000 kg m−3.

A Zero B 1.47 C 8.34 D 9.81

6 A heavy flagpole PQ is hinged at a vertical wall at end P and held in place by a wire connected to end

Q and a point R on the wall. The weight of the flagpole is W and the tension in the wire is T.

What is the direction of the force exerted by the wall on the flagpole if the flag pole is in equilibrium?

A PR B PS C PQ D PX

The forces must all pass through the same point for three forces to be in equilibrium (corollary forces)

displacement

time

D

A

B

C

ND

mgVgD

DmgVg

DmgU

34.8=−=

+=+=

ρρ

U

mg

D

6


W

F R

θ T

r

h

r - h F

W

( )22 hrr −−

7 A small ball of weight W is suspended by a light string. The

tension in the string is T. Two additional forces, F and R

act on the ball as shown in the diagram.

Which of the following equations is correct if the ball in

in equilibrium?

A WT =θsin B RFT −=θsin C FW =θtan D 222 WFT +=

This is obtained by summing forces in the horizonta l direction.

8 What is the force F required to be applied horizontally at the axle of a wheel of weight W and radius r,

in order to raise it over a curb of vertical height h?

A F = W B

rhW

F = C

( )hrrW

F−

= D ( )

( )hr

hrhWF

−−

=22

Taking moments about the curb, clockwise moment = anticlockwise moment F (r – h) = W

( )( )hr

hrh2WF

2

−−

=

r

h

( )22 hrr −−

7


9 Two identical helical springs are fixed to a body m1 of mass 1 kg. In another configuration, only one of

the springs is fixed to the mass. What is the ratio of the period of oscillation of set up (a) to set up (b)?

A 1:1 B 1:2 C 2 :1 D 2:1

1

22

2

11

2

1

)@(

1

)@(

==

=

=

+=−

k

m

k

m

T

T

kK

k

kkK

beff

aeff

10 A home made rocket is fired and it reaches a height of 100 m. If it has a mass of 50 kg, and has an

efficiency of 65%, what is the energy delivered in kJ from its fuel? (Assume fuel has negligible weight)

A 31.9 B 65.5 C 75.5 D 85.5

PE at highest elevation = mgh = 50(9.81)(100) = 49050 J Input power = PE/0.65 = 75.5 kJ

11

In the diagram given, the smaller gear spins in a clockwise direction and drives the larger gear.

Which of the following statements describing the motion of the resulting motion is true?

A The angular velocity of the two gears are equal

B The tangential velocity of the two gears are equal

8


C The angular velocity of the larger gear is higher.

D The tangential velocity of the bigger gear is higher.

12 The minimum speed with which a body of mass m should be projected from the Earth’s surface in order

to reach an infinite distance is about 1.1 x 104 m s-1. [This is called the escape speed.] Estimate the

escape speed in m s-1 for a body of mass 2m.

A 2.2 x 103 B 0.6 x 104 C 1.1 x 104 D 1.6 x 104

By Conservation of Energy, ½ mvE

2 – 0 = 0 – [-GMEm/RE] vE

2 = 2GME/RE ------ (1) Escape speed is independent of m escape speed for 2m is the same as that for m.

13 The graph below shows that variation of displacement with time for two particles performing simple

harmonic motions with the same frequency and amplitude.

What is the phase difference between the motions?

A 6

π B 4

π C 3

π D 2

π

62

12

2 ππφ ==

14 Which effect provides direct experimental evidence that light is transverse, rather than a longitudinal,

wave motion?

A Light can be diffracted.

B Two coherent light waves can be made to interfere.

C The intensity of light from a point source falls off inversely as the square of the distance from the

source.

D Light can be polarized.

Only transverse waves can be polarized.

2 4 6 8 10 12 14 16 18 20 22 24

9


15 In a Young’s double-slit experiment using monochromatic light of wavelength 564 nm, the fifth bright

fringe is observed at an angle of 0.32O to the central bright fringe. Calculate the slit separation in

metres.

A 2.8 x 10-6 B 1.0 x 10-4 C 5.0 x 10-4 D 2.5 x 10-3

mx

a

aD

xa

Dx

a

Dx

O

49

100.532.0tan

105645

tan

5

5tan

5

55

−−

×=×==

==

=

=

θλ

λθ

λ

λ

16 A water wave P is incident on a wall. A reflected wave Q moves away from the wall. The diagram

illustrates the position of P and Q at time zero.

X, Y and Z represent three separate positions of the resulting stationary wave.

In which order does this stationary wave have these positions, beginning at time zero?

A X Y Z Y

B Y X Y Z

C Y Z Y X

D Z Y X Y

Screen

Central bright fringe

5th bright fringe

0.32O

10


At time=0, there is destructive interference, and h ence starting point is Y. In the next

instant, wave Z is the resultant and hence answer i s C

17 The diagram below shows one of the wheels of a car which is about to go over a road hump. The

shock absorber system of the car will be damped critically after the wheel has gone over the hump.

Which graph represents the variation of vertical displacement x of the body of the car with time t after

the wheel has gone over the hump?

A

B

C

D

Part A shows free oscillations, B shows light dampi ng and D shows heavy damping. Only part

C shows critical damping.

18 A cell is connected in series with a 2 Ω resistor. Its internal resistance is 0.5 Ω. If the current in the

circuit is 3 A, what is the e.m.f. of the cell in V?

A 1.5 B 3.0 C 6.0 D 7.5

Total voltage across both resistances = e.m.f. = IR = 3(2+0.5) = 7.5 V

19 Which graph represents the I-V characteristic of a semiconductor diode?

A

B

C

D

11


20

A uniform electric field is produced between two parallel plates 10 mm apart. The potential difference

between the plates is 100 V. A point charge of 1 µC is transferred along a 10 mm diagonal path from X

to Y.

What is the work done in µJ by the electric field on the charge as the charge moves from X to Y?

A 10 µJ B 25 µJ C 50 µJ D 100 µJ

W = FE (s cos60°) = qE(s cos60°) = qV/d(s cos60°) = (1 x 100/10)(10 cos60°) = 50 µJ ]

12


SECTION B: STRUCTURED QUESTIONS

1 (a) During a laboratory class, Christopher used the vernier callipers to measure the diameter of a Styrofoam ball. He recorded the ball’s diameter as (5.28 ± 0.01) cm. Looking up the density table of materials, he found that the density of Styrofoam is 150 kg m-3.

(i) Calculate the mass, in kg, of the Styrofoam ball.

[2]

( )]1A[kg1016.1

1028.515061

]1M[d61

2d

34

r34

m

2

32

3

3

3

−

−

×=

×××π=

πρ=

πρ=

πρ=

(ii) Calculate the fractional uncertainty in the mass of the Styrofoam ball.

[2]

]1A[1068.528.501.0

3

]1M[dd

3mm

d61

m

3

3

−×=

×=

∆=∆

πρ=

(iii) Hence express the mass of the Styrofoam ball, together with its uncertainty, to an

appropriate number of significant figures.

[2]

]1M[kg1056.6

1016.11068.5m

1068.5mm

5

23

3

−

−−

−

×=×××=∆

×=∆

( ) kgmm 51071160 −×±=∆± [A1]

(b) Christopher then put the Styrofoam ball in a basin of water of density 1000 kg m-3 and observed

that the ball is floating on water.

(i) State the condition which must be satisfied in order for the Styrofoam ball to float on water.

[1]

Upthrust on Styrofoam ball = Weight of Styrofoam ball (Principle of Flotation) [B1]

13


(ii) Hence calculate the fraction of the Styrofoam ball submerged in water. [2]

]1A[15.01000150

f

]1M[gVgfV

WU

water

ball

ballwater

=

=

ρρ

=

××ρ=××ρ=

(iii) Describe what will happen when the Styrofoam ball is transferred into a basin of sea water.

[1]

Since density of sea water is greater than the density of fresh water, the fraction of Styrofoam ball submerged in water is less. [B1]

2 An C-130 transport aeroplane is flying horizontally at an altitude of 20 metres and it flies at a constant velocity of 50 ms-1. A supply package is dropped out of the the plane at the instant shown in the diagram below. Assume air resistance is negligible.

Figure 2

(i) What is the time taken for the package to reach the ground? [2]

stt

atuts

02.2)81.9(2

120

2

1

2

2

=⇒=

+=

M1

A1

(ii) What is the speed of the package just before hitting the ground? [2]

12222

1

77.538.1950

8.19)02.2(81.9

−

−

=+=+=

==+=

msvvv

msatuv

yx

y

M1

A1

(iii) What is the angle to the horizontal at which the package hits the ground? [2]

°== − 6.2150

8.19tan 1θ CCW from negative x direction.

M1 A1

150 −ms

m 20

14


(iv) Ignoring the effect due to air resistance sketch on the same graph showing how the horizontal and vertical velocities vary with time.

[2]

Assume downward direction is positive and left direction is positive as well.

B2 for shape.

(v) If the package was pushed backwards out of the plane at 2 ms-1 relative to the

plane, explain qualitatively how would your answer in part (i) and part (ii) be

affected?

[2]

Actual initial speed of package reduced to 48.

No change to part (i),

but reduces the resultant velocity in part (ii)

B1

B1

3 A red ball, of mass 0.3 kg and velocity 10 m s–1, collides elastically and head-on with a blue ball, of mass 0.2 kg and velocity 15 m s–1, moving in the opposite direction

(a) (i) State the law of conservation of momentum. [2] In an isolated system

Total momentum is conserved. B1 B1

(ii) State the condition for a collision to be considered elastic. [1] Kinetic energy is conserved. B1 (iii) What do you expect to see in the subsequent motion if the collision is head on. [1] Velocities before and after collision are in a straight line B1 (b) Find the relative velocity of separation of the two vehicles after the collision [2] 1

1221 25)15(10 −=−−=−=− msvvuu

(c) Hence, or otherwise, find the respective magnitude of the final velocities of the two balls [4]

12

11

1

11

12

21

22112211

15)10(25

10

5.05

)25(2.03.00

25

(b)part From

)(2.0)(3.0)15(2.0)10(3.0

−

−

=−+=

−=

=−++=∴

+=

+=−++=+

msv

msv

v

vv

vv

vv

vmvmumum

vertical

horizontal

50

19.8

15


4 During the National Day parade, the Black Knights performed a series of stunts for the audience.

In one such stunt, an F16 flies horizontally at a speed of 170 m s-1 before flying upwards in a

vertical loop, 1000 m high, as shown in the diagram below.

Figure 4

(a) Explain why a body in uniform circular motion must experience a resultant force. [2]

Speed is constant but direction is changing and hence the velocity is changing.

Hence there is an acceleration.

By Newton’s 2nd Law, if there is an acceleration, there is a resultant force.

B1

B1

(b) Draw fully labelled free body diagrams of the pilot, of mass 70 kg at;

1. Point A

2. Point B

[2]

B1 (for each

FBD with proper

labels. All forces must be present

and labelled)

(c) Show that the normal reaction force on the pilot is greater at Point A. (Assume that the

speed of the plane is constant in the whole loop).

[4]

At Pt A,

Nmgr

mvN

mgNr

mv

A 7.4732)81.9)(70(500

)170(70 22

2

=+=+=

−=

and at Pt B,

Nmgr

mvN

mgNr

mv

B 3.3359)81.9)(70(500

)170(70 22

2

=−=−=

+=

Since plane is moving at constant speed, N at pt B is smaller than at point A.

M1

M1

A1(for both correct

answers)

A1

B

1000 m

mg

N

Pt A

mg

N

Pt B

A

16


(d) Extra energy is required from the engine to maintain constant speed in the loop.

Suggest two possible reasons.

[2]

Work done against air resistance

Work done against gravity

B1

B1

5 (a) Explain the term simple harmonic motion. [2] Oscillatory motion such

that the acceleration is always proportional to (x0), the displacement from a fixed point. and it is directed always toward the fixed point.

B1 B1

(b) (i) State the defining equation for simple harmonic motion [1]

0

2xa ω−= A1

(ii) Write down a solution to the equation giving the displacement x in terms of the amplitude of oscillation x0, the angular frequency ω and the time t

[1]

txx ωcos0= A1

(c) The velocity v of a body of mass m undergoing simple harmonic motion is given by, 22 xxv o −±= ω

Find the kinetic energy of the body in terms of its displacement x, and ω and x0

[1]

)(

2

1

2

1 220

22 xxmmvKE −== ω A1

(d) Sketch two separate graphs, to show how the velocity and kinetic energy vary with the displacement of a body undergoing simple harmonic motion.

[3]

(B2 for shape)

(B1 for correct

labelling)

17


6 This question is about the physics of seismic waves. When an earthquake occurs, two kinds of seismic wave travel from their source through the body of the earth. Primary or P waves have the greater speed and are longitudinal. The slower Secondary or S waves are transverse.

(a) The diagram shows a Secondary wave approaching a tall building from underneath. Copy and indicate, with a double-headed arrow, in which direction you would expect the building to vibrate when the wave reaches it.

Figure 6.1

[1]

B1

(b) The centre of an earthquake produces both longitudinal waves (P waves) and transverse waves (S waves). The graph below shows the variation with time t of the distance d moved by the two types of wave. d / km

t / s

P wave S wave1200

800

400

00 25 50 75 100 125 150 175 200 225

Use the graph to determine the speed of

(i) The P waves [1]

196005.62

600000 −== msspeed A1

(ii) The S waves [1]

158185.137

800000 −== msspeed A1

18


(c) The waves from an earthquake close to the Earth’s surface are detected at three laboratories L1, L2 and L3. The laboratories are at the corners of a triangle so that each is separated from the others by a distance of 900 km, as shown in the diagram below.

L L

L

1 2

3

900 km

Figure 6.2

The records of the variation with time of the vibrations produced by the earthquake as detected at the three laboratories are shown below. All three records were started at the same time.

time

start of trace

L

L

L

1

2

3

Figure 6.3

On each record, one pulse is made by the S wave and the other by the P wave. The separation of the two pulses is referred to as the S-P time interval. The S-P time intervals are 68 s, 42 s and 27 s for laboratories L1, L2 and L3 respectively.

(i) Use the formula “speed = distance / time” to write an expression for the distance, in m, traveled by the P waves, dp, from the source to station L1.

[1]

ttspeedd Pp 9600==

(ii) Hence write an expression for the distance traveled by the S waves, ds, from the source to the L1 seismological station.

[1]

)68(5818)( +=+= tttspeedd SPSS

(iii) Given that dp = ds, calculate the time taken for the P waves to travel from the source to the L1 seismological station.

[1]

st

tt

6.104

)68(58189600

=+=

(iv) Hence determine the distance from the source to L1. [1]

kmtspeedd Pp 1004)6.104(9600 ===

19


(v) Hence, derive a formula that you can use to determine the distance from the source to L1, in terms of vP (the speed of the P wave), vS (the speed of the S wave), and tSP (the S-P time interval).

[1]

kmtt

vv

tvvtvd

vv

tvt

ttvtv

SPSP

sp

SPSPpp

sp

SPS

SPsp

768.1458189600

)5818)(9600(

)(

=−

=

−==

−=

+=

(vi) Determine the distance from the source to the seismological station for L2 and L3. [2]

kmd

kmd

L

L

398)27(768.14

620)42(768.14

3

2

====

(vii) Copy diagram A and show how you could determine a possible site of the epicenter of the earthquake. (label the point E)

[2]

L L

L

1 2

3

900 km

(B1 for arcs drawn)

B1 for correct location (rough)

(viii) State one assumption made in this method of calculation that might lead to inaccurate results.

[1]

The calculation assumes the earthquake originates at the surface of the Earth instead of below the surface.

B1

7 (a) State what is meant by

(i) an electric field of force, [1]

(ii) a gravitational field of force. [1]

[(a)(i) An electric field of force is a region around an electric charge in which an electric force is exerted on another electric charge. [B1] (a)(ii) A gravitational field of force is a region around a body of finite mass in which a gravitational force is exerted on another body of finite mass. [B1]

(b) Two ions A and B are separated by a distance of 0.80 nm in a vacuum, as shown in Figure

7.1. A has a charge of +3.2 x 10-19 C and B has a charge of -1.6 x 10-19 C. A point X is positioned vertically above B, at a distance 0.50 nm. Copy Figure 7.1 and draw labeled arrows to represent

(i) the electric field EA at the point X due to A only,

[1]

(ii) the electric field EB at the point X due to B only.

[1]

E

20


[(i) arrow points away from A; arrow should be along the line joining A and X. [B1] (ii) arrow points towards B; arrow should be along the line joining B and X. [B1]

(iii) the resultant field E at the point X.

[1]

[Completes vector diagram to show magnitude and direction of E. Makes use of answer in d(i) for direction. [B1] ]

(c) (i) Sketch on the diagram in (b), lines representing the electric field between the two ions. Include the field line passing through X.

[4]

[no. of field lines leaving A is twice that terminating at B. [B1] Shape of field lines. [B1] Direction of field lines. [B1 ] Field line at point X is tangential to E drawn in (d)(ii). [B1 ]

(ii) Indicate clearly on the diagram in (b), the position of the null point (where electric field is zero, other than at infinity).

[1]

Null point is to the right of charge -q B1

(iii) Explain why the null point exists at this position [1]

Null point exists because at this point, the Electric force from +2q and that of –q cancel

each other out.

B1

(d) (i) Find the magnitude of the electric force that A exerts on B. [2]

A B

X

0.80 nm

0.50 nm

Figure 7.1

21


[FE = QAQB/4πεor2 [M1]

= 7.19 x 10-10 N [A1] ]

(ii) Explain quantitatively why the gravitational force is usually not considered at the atomic scale. mass of A, mA = 5.81 x 10-26 kg mass of B, mB =3.98 x 10-26 kg

[3]

[FG = GmAmB / r2 [M1] = 2.41 x 10-43 N [A1] Ratio FE/FG = 2.98 x 1033 The electric force is about 33 orders of magnitude stronger than the gravitational force. Hence the gravitational force is negligible compared to the electric force. [B1 – for comparing] (e) Figure 7.2 shows two identical conducting spheres of uniform density. Each sphere has mass

M and carries an overall charge +Q. They are placed in a vacuum with their centres distance

d apart. When the two conductors are brought into this set up, the charges redistribute as

shown in the diagram.

(i) Explain why the electric force FE between them the two conductors cannot be found using the equation below.

2

2

4 d

QF

oE πε

=

[1]

The net effect of the charges does not act through the center of the spheres. The expression above can be used only to find the electric force between point charges or between bodies with a spherically symmetric charge distribution. [B1]

(ii) Suggest a condition under which the electric force FE between them may be

approximated by the expression in (e)(i).

[1]

When the spheres are separated by an infinitely large distance. [B1] OR when the distance between the conductors is infinitely larger than the diameter of the conductors. (iii) Explain whether the expression below can be used to calculate the gravitational force

between the spheres.

2

2

dGM

FG =

[2]

[Yes. This expression is valid for point masses or bodies with a spherically symmetric mass distribution. The gravitational force exerted by a body with a spherically symmetric mass distribution on a particle outside is the same as if the entire mass were concentrated at the centre. [B1] The redistribution of the electrons on the spheres does not cause a significant change in the mass distribution since electrons are of negligible mass. Hence the expression can be used. [B1] ]

d

Figure 7.2

+ + + +

+ + + +

22


8 (a) In a Young’s double-slit experiment, coherent light from two slits 1S and 2S falls on a screen 800 mm beyond the slits. The distance between the centres of the slits is 0.600 mm. There is a central bright fringe at O and the third bright fringe is formed at P, 2.00 mm away from O.

Figure 8.1

(i) Show that the distance S1P is 800.0018 mm

[1]

Using Pythagoras’ theorem, mm0018.800PS,80070.1PS 1222

1 =+= [A1]

(ii) Show that the distance S2P is 800.0033 mm

[1]

Using Pythagoras’ theorem, mm0033.800PS,80030.2PS 2222

2 =+= [A1]

(iii) By considering the path difference S2P - S1P, hence calculate the wavelength of light used.

[2]

S1

S2

0.600 mm O

P

800 mm

2.00 mm

0.300 mm

S1

S2

0.600 mm O

P

800 mm 0.300 mm

1.700 mm

S1

S2 O

P

2.00 mm

23


P is the 3rd bright fringe, hence path difference is equal to 3 wavelengths.

Path difference = λ=− 3PSPS 12 [M1] 800.0033 – 800.0018 = 3λ λ = mm1000.5 4−× = 500 nm [A1]

(b) A spectrometer and diffraction grating were set up to study the Balmer series of the hydrogen spectrum. The emission spectrum of an element was viewed in the second order and visible lines were observed. The angular positions of these lines measured against the scale on the spectrometer are shown in the table. Angular position of the zero order = 126.4O Number of rulings per unit length = 450 000 lines per m

Figure 8.2

(i) Calculate the wavelength of the violet line from the angular position given.

[2]

O

OO

67.21

4.12607.148

=−=θ

15 m105.4N −×=

]1A[m1010.4

]1M[2105.4

67.21sinNnsind

nN

sin

nsind

7

5

O

−×=××

=

θ=λ

λ=θλ=θ

(ii) Calculate the maximum number of violet lines possible. [2]

For highest order, θ = 90O

]1M[51010.4

90sin1022.2

sindn

nsind

7

O7

=×

××=

λθ=

λ=θ

−

−

Maximum number of violet lines observed = 2 x 5 + 1 = 11 [A1]

24


(iii) State one advantage and one disadvantage of using the larger order spectrum instead of the first order spectrum.

[2]

Advantage: The angle of diffraction for the larger order spectrum is larger than that of the first order spectrum, therefore there is less percentage uncertainty in the measurement of the angle for a given precision of the measuring instrument. [B1] Disdvantage: The intensity of the larger order spectrum is lower than that of the first order spectrum. [B1]

9 (a) State the difference between e.m.f. and potential difference. [2]

Rate of energy converted from non-electrical to electrical when 1 C of charge is delivered a circuit while the potential difference is the energy dissipated when 1 C of charge flows between two points.

B1 B1

(b) How many electrons pass a point in 3 minutes when the current flowing is 3 A? [2] Q=It = 3(3)(60) = 540 C

540 = Ne

N= 2119

1038.3106.1

540540 ×=×

= −e

M1

A1

(c) A 5 V rated battery is connected with a switch in series with a component that has an effective resistance of 2 Ω. If the battery has an internal resistance of 0.5 Ω,

(i) State the electromotive force delivered by the battery? [1]

Emf = 5V A1

(ii) Calculate the terminal potential difference when the switch is closed? [1]

VV 45

5

45

5.02

2 ==+

=

A1

(iii) Calculate the power dissipated at the component? [2]

Total resistance = Ω=+ 5.25.02

I= AR

V2

5.2

5 ==

Power = WRI 8)2(222 ==

M1

A1 (iv) Calculate the power loss in the battery? [2]

Power loss = WrI 2)5.0(222 == M1 A1

25


End of Paper

End of Paper

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