2010H2Physics RI

RAFFLES INSTITUTION 2010 Preliminary Examination

PHYSICS Higher 2 Paper 1 Multiple Choice

9646 / 01 9745 / 01

24 September 2010 1 hour 15 minutes

Additional Materials: OMR form Soft clean eraser Soft pencil (type B or HB is recommended)

READ THESE INSTRUCTIONS FIRST Do not open this booklet until you are told to do so. Fill in your particulars on the OMR form. There are forty questions in this paper. Answer all questions. For each question there are four possible answers A, B, C and D. Choose the one you consider correct and record your choice in soft pencil on the OMR form. Read the instructions on the OMR form very carefully. Each correct answer will score one mark. A mark will not be deducted for a wrong answer. Any rough working should be done in this booklet.

This booklet consists of 22 printed pages including the cover page.

www.erwintuition.com


2

Data

speed of light in free space, c = 3.00 x 108 m s−1

permeability of free space, µ0 = 4π x 10−7 H m−1

permittivity of free space, ε0 = 8.85 x 10−12 F m−1

(1 / (36 π)) x 10−9 F m−1

elementary charge, e = 1.60 x 10−19 C

the 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

Formulae

uniformly accelerated motion, s = 212

ut at+

2v = 2 2u as+

work done on/by a gas, W = p∆V

hydrostatic pressure, p = ρgh

gravitational potential, φ = Gm

r−−−−

displacement of particle in s.h.m., x = x0 sin ω t

velocity of particle in s.h.m., v = v0 cos ω t

= ( )2 2

0x xω± −

mean kinetic energy of a molecule of an ideal gas E =

3

2kT

resistors in series, R = R1 + R2 + …

resistors in parallel, 1/R = 1/R1 + 1/R2 + …

electric potential, V = 4

Q

rε0π

alternating current/voltage, x = x0 sin ω t

transmission coefficient, T = exp(−2kd)

where k =

(((( ))))2

2

8 m U E

h

π −−−−

radioactive decay, x = x0 exp (−λt)

decay constant, λ = 12

0.693

t



4

1 The coefficient of viscosity, η, for a fluid is given by:

FLη =

Av

where F is the external force on the fluid, v is the relative motion of the fluid layers, L and A

are the width and area of the fluid layer respectively. The base units for η are

A N s-1 m-2 C kg m s-1

B N s m-2 D

kg m-1 s-1

2 Estimate the number of atoms in 1 cm3 of a solid.

A 1010 C 1030

B 1024 D

1040

3 At time t = 0 s, a ball was released from rest above a floor. In the velocity-time graph shown

below, at which time does the ball reach its maximum height after bouncing from the floor?

velocity v

time t A

B

D C 0



5

4 Consider a falling raindrop undergoing constant acceleration. Which pair of quantities would

yield a straight line graph when plotted to represent the motion of the raindrop?

A Velocity of the raindrop and its displacement.

B Displacement of the raindrop and its time in motion.

C Kinetic energy of the raindrop and its displacement.

D Kinetic energy of the raindrop and its time in motion.

5 Two particles of identical masses are initially projected towards each other on a smooth

surface with speeds u1 and u2 respectively. They collide elastically with each other, and their

directions and speeds after the collision are shown in the figure below.

Which one of the following equations cannot be applied to the collision of this system?

A u1 - u2 = v2 + v1 C u1

2 – u2

2 = v1

2 + v2

2

B u1 + u2 = v2 – v1

D

u1

2 + u2

2 = v1

2 + v2

2

6 A movable notice-board of mass 2.0 kg is placed on a smooth floor. What is the initial

acceleration of the notice-board when a horizontal stream of water, travelling at speed

8.0 m s-1, strikes it at a rate of 1.0 kg s-1 for a duration of 50 s.

A 0.16 m s-2 C 4.2 m s-2

B 4.0 m s-2 D

8.0 m s-2

u2

Before collision

u1

v2

After collision

v1



6

7 A pendulum bob is suspended in a bus of mass 3000 kg undergoing constant deceleration.

The pendulum makes an angle of 18° with the vertical. What is the deceleration of the bus?

A 0.32 m s-2 C 3.2 m s-2

B 3.0 m s-2 D

9.3 m s-2

8 A clown on a unicycle accelerates to the left.

What is the direction of the resultant force due to the road acting on the wheel of the

unicycle?

A

C

B

D

9 A 1.6 kg block slides down a plane that is inclined at 25° with the horizontal, at a constant

speed of 2.0 m s-1. At what rate is the frictional force doing work on the block?

A -28 W C 13 W

direction of motion

road

18° direction of motion



7

B -13 W D

28 W

10 A 100 kg crate is pulled from rest across a floor with a constant force of 320 N. For the first

20.0 m, the floor is frictionless and for the next 10.0 m, a constant frictional force of 30.0 N

acts on the crate. What is the final speed of the crate?

A 8.00 m s-1 C 13.6 m s-1

B 8.37 m s-1 D

13.9 m s-1

11 A car travels on a curved track of radius 150 m. The track is banked at an angle of 15o. At

what speed must the car travel such that friction is not required for it to travel safely in the

circular path?

A 13 m s-1 C 28 m s-1

B 20 m s-1 D

38 m s-1

12 A roller coaster starts from rest on a hill-top. It accelerates along a frictionless track and

enters a loop-the-loop of radius 60 m as shown below.

60 m

H

In order for the roller coaster to just remain in contact with the track when it is at the top of the

loop-the-loop, the vertical height H between its starting point and the entrance of the loop-the-

loop must be

A 90 m

C 150 m

H



8

B 120 m

D

180 m

13 A rock is thrown vertically upward near the surface of Planet X with a velocity of 45 m s-1 and

it comes to an instantaneous rest 5.2 s later. If the same rock is now thrown up near the

surface of Planet Y with the same initial velocity as that on Planet X, at 5.2 s later it is still

moving upwards at a speed of 25 m s-1. If both planets do not have atmosphere, the ratio of

the gravitational field strength near the surface of Planet Y to that of Planet X is

A 0.25

C 0.44

B 0.38

D

0.62

14 Suppose a planet has radius R and mass M. An object of mass m is moved from the surface

of the planet to a height h above the surface, where the planet’s gravitational field is

negligible. What is the change in gravitational potential energy of the object?

A GMm

R h−

+

C GMm

R h+

B GMm

R−

D

GMm

R

15 A body in simple harmonic motion makes n complete oscillations in 1.0 min. What is the

angular frequency ω of this motion?

A

1 rad s60

n −

C 1 rad s

30

nπ −

B 1 rad sn− D

12 rad snπ −



9

16 A mass of 2.0 kg is executing simple harmonic motion. The net force F acting on the mass

varies with displacement x as shown. What is the maximum speed of the mass?

x/ m0 0.2

F/ N

0.40.20.4

4

8

4

8

A 11.0 m s− C 11.3 m s−

B 11.4 m s− D 12.0 m s−

17 Four different solids A, B, C and D of equal masses at 20 C° are separately heated at the

same rate. Their melting points and specific heat capacities are as shown in the table below.

Which of these solids will start to melt first?

Liquid Melting point/ °C Specific heat capacity/ J kg−1 K−1

A 80 1200

B 100 800

C 150 600

D 300 250

18 The piston of a gas-tight syringe containing an ideal gas is pulled outwards quickly. Which of

the following changes is incorrect?

A The density of the ideal gas decreases.

B The pressure of the ideal gas decreases.

C The temperature of the ideal gas decreases.

D The root-mean-square speed of the atoms increases.



10

19 Which of the following statements about electromagnetic waves is not true?

A They can be polarised.

B They are transverse waves.

C They always travel at 8 -13 0 10 ms. × .

D They are diffracted when they pass through a small aperture.

20 Some fine sand particles are present in a long transparent tube. A speaker is placed at the

end of the tube, and the frequency of the sound emitted is varied until the fine sand settles

into a series of small heaps. The diagram below shows a section of the tube and some of the

heaps that were formed.

Which of the following statements is true?

A The air molecules are vibrating vertically.

B The wavelength of the sound is given by L.

C The air pressure where the heaps are is the lowest.

D The positions of the heaps show the positions of the displacement nodes.

L



11

21 A horizontal steel wire is fixed at one end and is kept under tension by means of weights

suspended over a pulley. The length of wire between the fixed end and the pulley is 1.0 m.

Magnets are placed near the centre of the wire, and an alternating voltage supply is

connected to the wire between the fixed end and the pulley. Standing waves are formed when

the voltage supply is turned on. Five antinodes are observed on the wire.

Given that the speed of the wave on the wire is 24 m s-1, what is the frequency of the voltage

supply?

A 48 Hz C 96 Hz

B 60 Hz D

120 Hz

22 In a diffraction grating experiment, the first order image of a 438 nm blue light occurred at an

angle of 16.2°. A second order coloured light was observed at 47.4°. What is the wavelength

of this coloured light?

A 578 nm C 637 nm

B 631 nm D 696 nm

N

S

1.0 m

Fixed end

pulley

weights



12

23 Two charges + 2q and – q are placed at a distance 2d apart. The electric potential at X, a

distance d away from – q is

A

04

q

dπε

− C 2

036

q

dπε

−

B

012

q

dπε

− D

2

0

7

36

q

dπε

−

24 The diagram shows two plates J and K, a distance 0.080 m apart in a vacuum. An electron,

originally at rest, is accelerated by a uniform electric field of 5 13.0 10 N C−× from K to J. What

is the gain in the electron’s kinetic energy?

A 264.3 10 J−× C 144.8 10 J−×

B 153.8 10 J−× D 136.0 10 J−×

Plate J

Plate K

0.080 m

Electron moving

towards J

+ 2 q – q X

2 d d



13

25 Eight small conductors of charge Q are placed on the edge of an insulating disc of diameter

D. The angular frequency of rotation of the disc isω .

What is the equivalent electric current at the edge of the disc?

A

4Qω

π C 8Qω

B

8Q

D

ω

π D

16Qπ

ω

26 A car battery of e.m.f. 12 V and internal resistance 0.020 Ω is connected to a load of 4.0 Ω. If

the potential difference across the load is 10 V, what is the power lost in the connecting

wires?

A 0.13 W C 4.9 W

B 1.0 W D

5.0 W

D

Q

Q

Q

Q

Q Q

Q

Q



14

27 Five resistors of equal resistance are connected as shown.

Which two points would give the maximum combination resistance?

A PQ C PS

B PR D

QS

28 The diagram below shows a simple potentiometer circuit used to determine the internal

resistance of a cell of e.m.f. E. The driver cell has an e.m.f. of 2.0 V with negligible internal

resistance and the metre wire PQ is 1.0 m long. The cell is connected in parallel with a

resistor of 2.0 Ω. When the switch is open, the balance length is 0.70 m and when the switch

is closed, the balance length is 0.50 m.

What is the internal resistance of the cell?

A 0.15 Ω C 0.50 Ω

2.0 V

P

2.0 Ω

Q

Switch S

r E

P

R

Q S



15

B 0.40 Ω D

0.80 Ω

29 Wire 1 carries a current of 4.2 A to the right as shown in the figure below. What is the

magnitude and direction of the current that is carried in Wire 2 so that the net magnetic flux

density at point A is 4.0 x 10-6 T.

10 cm

5 cm

The magnetic flux density at a perpendicular distance r from a straight current-carrying

conductor is given by 2

oB

r

µ

π=

I, where I is the current in the conductor.

A 0.40 A to the left C 1.4 A to the left

B 0.40 A to the right D

1.4 A to the right



16

30 One end of a flat rectangular coil of negligible mass is placed at the centre of a 1000-turn

circular coil of diameter 25 cm as shown in the figure below. A current of 5.0 A is passed

through the rectangular coil and when a 5.0 g paper rider is placed at 2.0 cm to the right of

the pivot, the rectangular coil is balanced horizontally. What is the magnitude of the current

that the 1000-turn circular coil must carry in order for the rectangular coil to remain

horizontal?

4.0 cm

The magnetic flux density at the centre of a flat circular coil of N turns and radius r is given by

oN

Br2

µ=

I where I is the current carried in the coil.

A 3.3 A C 6.5 A

B 5.0 A D

9.0 A



17

31 Large alternating currents in a straight conductor can be measured by the e.m.f. induced in a

small coil. Which of the following arrangements of the coil induces the largest e.m.f.?

A B C D

32 A right-hand drive car heads East at a speed of 20 m s-1. It cuts the vertical component of the

Earth’s magnetic field of flux density 5.0 X 10-5 T acting downwards. Taking the width of the

car’s bonnet to be 1.5 m, what is the e.m.f. generated across the bonnet and which side of the

car will be positive?

E.m.f. generated Side of car which is positive

A 0.67 mV Driver

B 0.67 mV Passenger

C 1.5 mV Driver

D 1.5 mV Passenger

33 An alternating current I in amperes in a load resistor of 8.0 Ω varies with time t in seconds

according to the equation:

I = 5.0 sin(100πt )

Which of the following is the mean power dissipated in the resistor?

A 40 W C 100 W

B 50 W D

200 W



18

34. A transformer steps up 120 V at the primary coil to 240 V at the secondary coil. If the

current in the primary coil is 2.0 A and the power loss in the windings and core of the

transformer is 48 W, what is the current in the secondary coil?

A 0.2 A C 1.0 A

B 0.8 A D

1.2 A

35 In a photoelectric emission experiment, a metal is irradiated with photons of wavelength λ.

The minimum frequency to cause photoelectric emission is f0. If c is the speed of light, what

fraction of the photon energy is converted to kinetic energy in the electron travelling with the

greatest speed?

A

0f c

λ

λ −

C 01f c

λ−

B

0

c

c f λ−

D

01f

c

λ−

36 The figure below shows the wave function ψ(x) of an electron.

P 0 Q

Which of the following statements is correct?

A The probability of locating the electron at x = 0 is the highest.

B ( )2

xψ is the probability of locating the electron within a given region.

C There is greater probability of locating the electron on the left of the vertical axis.

D The probability of locating the electron between positions P and Q is ( )

2Q

P

x dxψ∫ .

ψ(x)

x



19

37 Which of the following about doped semiconductors is correct?

Charge of semiconductor Majority charge carriers

p-type positive holes A

n-type negative electrons

p-type neutral holes B

n-type neutral electrons

p-type positive protons C

n-type neutral neutrons

p-type neutral protons D

n-type neutral electrons

38 The figure below shows how the potential V(x) varies with the distance x across a p-n

junction.

Which of the following graphs correctly shows the variation of V(x) when reverse bias is

applied across the p-n junction?

V(x)

x



20

A

B

p - type

n - type

V(x)

x

n - type

p - type

V(x)

x



21

C

D

n - type

p - type

V(x)

x

p - type

n - type

V(x)

x



22

39 Two samples of radioactive nuclides X and Y are prepared. Y has twice the initial

activity and twice the half-life of X. After 6 half-lives of X, what is the ratio of the activity

of X to Y?

A

1

2 B

1

4 C

1

8 D

1

16

40 The nuclear reaction P Q X Y+ → + proceeds with a release of energy. Which of the

following statement must be correct?

A Mass of X and Y is larger than mass of P and Q.

B Momentum of X and Y is larger than momentum of P and Q.

C Total binding energy of X and Y is larger than total binding energy of P and Q.

D Binding energy per nucleon of both X and Y are larger than binding energy per nucleon of P or Q.

END OF PAPER



Centre Number Index Number Name Class

RAFFLES INSTITUTION

2010 Preliminary Examination

PHYSICS

Higher 2

Paper 2

9646 / 02

21 September 2010

1 hour 45 minutes

Candidates answer on the Question Paper.

No Additional Materials are required.

READ THESE INSTRUCTIONS FIRST

Write your Centre number, index number, name and class in the spaces provided at the top of this page. Write in dark blue or black pen. You may use a soft pencil for any diagrams, graphs or rough working. Do not use staples, paper clips, highlighters, glue or correction fluid. Answer all questions. Write your answers in the spaces provided in this booklet. The number of marks is given in brackets [ ] at the end of each question or part question.

For Examiner’s Use

1 / 5

2 / 9

3 / 7

4 / 7

5 / 7

6 / 7

7 / 18

8 / 12

Total / 72

This booklet consists of 20 printed pages including the cover page.



2

DATA

speed of light in free space, c = 3.00 x 108 m s−1

permeability of free space, µ0 = 4 π x 10−7 H m−1

permittivity of free space, ε0 = 8.85 x 10−12 F m−1

elementary charge, e = 1.60 x 10−19 C

the 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

FORMULAE

uniformly accelerated motion, 212

s ut at= +

2 2 2v u as= +



gravitational potential, Gm

rφ = −

displacement of particle in s.h.m., 0 sinx x tω=

velocity of particle in s.h.m., 0 cosv v tω=

2 2

0x xω= ± −

mean kinetic energy of a molecule

of an ideal gas, E kT3

=2

resistors in series, R = R1 + R2 + . . . .

resistors in parallel, 1/R = 1/R1 + 1/R2 + . . . .

electric potential, V = Q/4πε0r

alternating current/voltage, x = x0 sinωt

transmission coefficient, T = exp(−2kd) where k =

2

2

8 ( )m U E

h

π −

radioactive decay, x = x0 exp(−λt)

decay constant, 12

0.693

tλ =



4

Answer all questions in the spaces provided.

1 A cylindrical thermos flask is used to store hot water. The internal diameter and depth of the thermos flask are measured to be (8.50 ± 0.01) cm and (17.0 ± 0.1) cm respectively.

(a) State the instrument used to measure its diameter and a systematic error that can occur with the use of this instrument.

[2]

(b) Calculate the capacity of the thermos flask and its associated uncertainty.

Volume = cm3 [3]



5

2 (a) A mass hanging from a spring balance in air gives a reading of 50 N. When the mass is completely immersed in water, the reading on the balance is 40 N. It is now completely immersed in another liquid, giving a reading of 34 N. Calculate the density of this liquid. Assume that the density of water is 1000 kg m-3.

Density = kg m-3 [2]

(b) In Fig. 2 below, a uniform beam of length 10.0 m and weight 500 N is hinged to a wall at point O. Its far end is supported by a cable that makes an angle of 53.0° with the horizontal. A 70.0 kg worker stands on the beam.

(i) Draw a labelled diagram showing the forces acting on the beam.

[2]

O

beam

cable

53.0°

s

Fig. 2



6

(ii) The worker walks towards the far end of the beam from O. Calculate the furthest distance s he can walk if the maximum possible tension in the cable is 1000 N.

s = m [2]

(iii) Calculate the magnitude of the force exerted by the hinge on the beam when the tension in the cable is 1000 N.

Reaction force = N [3]



7

3 (a) Gravitational field strength g and gravitational potential φ at a point due to a

spherical body are related by the equation gr

φ= −

d

d

where r is the distance

from the centre of the body to the point. Explain the significance of the negative

sign.

[1]

(b) Given the mass of Earth is 5.98 x 1024 kg and its radius is 6370 km, determine the minimum kinetic energy required to project a spacecraft of mass 2550 kg from the surface of Earth so that it completely escapes from the gravitational field of Earth. Ignore air resistance.

Minimum energy = J [3]

(c) As a spacecraft falls towards Earth, it loses gravitational potential energy. State the energy conversions for the spacecraft when it is falling through Earth’s atmosphere at constant speed.

[1]

(d) An astronaut in a spacecraft orbiting around Earth can be said to experience weightlessness. Explain why this is not true weightlessness.

[2]



8

4 (a) Explain what is meant by internal energy of a gas.

[1]

(b) A cylinder fitted with a piston contains 0.20 mole of an ideal gas. Initially the

volume and pressure of the gas are 3 35.0 10 m−× and 51.0 10 Pa× respectively.

(i) Calculate the initial temperature of the gas.

Initial temperature = K [2]

(ii) The gas is

(1) heated at constant volume to twice its initial temperature

(2) cooled at constant pressure to its initial temperature, and finally

(3) expanded isothermally to its initial volume.

Sketch the above changes on a clearly labelled p-V diagram.

[4]



9

5 Two small identical styrofoam balls of mass 0.50 g and charge +15 nC are placed in a hemispherical bowl of radius R with frictionless, non-conducting walls. At equilibrium, they are at a distance of 0.50R apart as shown in Fig. 5.

Fig. 5

(a) (i) Show that 14.5θ ≈ ° . [1]

(ii) On Fig. 5, indicate all the forces acting on one of the balls in the bowl. [2]

(iii) Hence determine the radius R of the bowl.

R = cm [3]

(b) State the effect on θ if the Styrofoam balls are replaced with metal ones of the same size and charge.

[1]

R R

0.50 R

hemispherical bowl

2θ



10

6 Fig.6.1 shows the front view of a large flat circular coil connected to a sinusoidal alternating voltage supply and a small flat circular coil placed at the centre of the large coil such that the planes of the two coils are coincident. The smaller coil is connected to a cathode-ray oscilloscope (c.r.o).

large coil small coil

Front view

Fig.6.1

(a) If the variation of the sinusoidal alternating current to the large coil is as shown in

Fig.6.2, draw sketch graphs, one in each case, to show the variation with time of

(i) the magnetic flux through the small coil and

(ii) the induced e.m.f. in the small coil as displayed on the c.r.o..

[2]

Current In large coil time Fig.6.2 Magnetic flux through small coil time Induced e.m.f in small coil . time

To a.c. supply To c.r.o.



11

(b) Justify the shape of your sketches in (a).

[3]

(c) State and explain how the trace on the screen of the c.r.o. would be affected if the small coil is rotated such that the angle between the planes of the two coils increase from zero to 900 whilst maintaining a constant root mean square current in the large coil.

[2]



12

7 Radiation is a significant component of heat transfer in buildings, especially for sun-exposed surfaces and regions of large temperature differences. Most countries have building regulations that contain instructions about limiting heat transfer in order to reduce the amount of heating or air-conditioning required.

In order to calculate heat transfer, a thermal transmittance coefficient or U-value is

measured for each type of building material. Mathematically, P

UA T∆

= where P is the

rate of heat transfer in watts, A is the surface area of the structure and T∆ is the air temperature difference between each side of the structure in Kelvin. The U-values of three construction components are given below:

Component U-value / W m-2 K-1

Single-glazed window 5.6

Double-glazed window 3.2

Uninsulated roof 1.9

A house has windows of total area 24 m2 and a roof of area 60 m2. On average, the owner heats the house for 3000 hours per year to a temperature that is 14 K above that of the air outside.

(a) (i) Calculate the amount of energy lost in a year through single-glazed windows.

Energy loss = kWh [3]

(ii) By installing double-glazed windows, calculate the owner’s annual savings if electricity costs $0.25 per kWh.

Savings = $ [3]



13

(b) The roof is now insulated with two 50 mm thick layers of thermal insulation on each side to reduce heat transfer, as shown in Fig. 7 below.

Fig. 7

U-value for thermal insulation 50 mm thick = 1.4 W m-2 K-1 To calculate the rate of heat transfer P through such a roof, a composite U-value, Uc, has to be used. Uc can be expressed in terms of the U-values of the individual materials by the equation

1 2

1 1 1.....

CU U U

= + +

(i) Using the above equation, show that the rate of heat transfer P through the roof with thickness of thermal insulation on each side t = 50 mm is 430 W.

[1]

t



14

(ii) Complete the table below for the different values of t. Leave your answers for P to 2 significant figures.

t / mm P / W

50 430

100

150

200

[2]

(iii) Using the data from the table, plot a graph of P against t. [2]

P/ W

10050 150 200 250

thickness of thermal insulation on each side/ mm

(iv) Explain why the rate of heat transfer for a thickness of 250 mm thermal insulation on each side cannot be accurately determined from the above graph.

[1]

100

300

200

400



15

(c) External work is required to get heat to flow from a cold reservoir to a hot reservoir.

A heat pump is such a device, which applies external work W to extract an amount

of heat QC from a cold reservoir, and delivers heat QH to a hot reservoir, as shown

in the illustration below.

Thermal efficiency, e, of a heat pump is defined as the ratio of W to QH during one

cycle of the process. W, which is equivalent to H C(Q -Q ), maintains a particular

temperature difference between the hot and cold reservoirs.

Effectiveness of a heat pump can be described in terms of its coefficient of performance, COP, given by the relationship:

1COP(heating mode)

e=

The graph below shows the relationship between thermal efficiency, e, of an ideal heat pump and the temperature of the hot reservoir, Th, for a temperature difference of 27 K.

x

x

x

x

x



16

(i) The house loses energy at a rate of 5.00 kW when the interior temperature is 287 K and the outside temperature is 260 K. Assuming a heat pump operates with a coefficient of performance that is 60.0% of the ideal value, calculate the electric power the heat pump needs to maintain the interior temperature at 287 K.

P W [3]

(ii) Electric resistance heaters convert all of the electrical energy supplied to internal energy. Explain why heat pumps are preferred over electric resistance heaters.

[2]

(iii) Give an example of an everyday household appliance that behaves like a heat pump.

[1]



17

It is recommended that you spend about 30 minutes on this question.

8 Light-dependent resistors or LDRs are used in light sensor circuits. The resistance of a LDR is very high when the surrounding is dim and very low when it is illuminated with light.

A student wishes to investigate how the resistance of a LDR varies with the amount of light falling on it. The LDR has a resistance of 100 Ω when it is in bright light and a

resistance of 500 kΩ when no light falls on it.

Design a laboratory experiment to investigate how the resistance of the LDR depends on the intensity of the illumination incident on the LDR.

You may assume that the following apparatus is available, together with any other standard equipment which may be found in a college science laboratory:

electric light bulb

rheostat

light-dependent resistor (LDR)

light meter with light intensity sensor

digital multimeters

dry cells

connecting wires

black cardboard tube

You should draw diagrams to show the arrangement of your apparatus and important electrical connections. In your account you should pay particular attention to

(a) the procedure to be followed,

(b) the measurements that would be taken,

(c) the control of variables,

(d) how the data would be analysed,

(e) any safety precautions that you would take.

[12]



18

Diagram



19



20

End of Paper



Centre Number Index Number Name Class

RAFFLES INSTITUTION 2010 Preliminary Examination

PHYSICS Higher 2 Paper 3 Longer Structured Questions

9646/03 9745/03

15 September 2010 2 hours

Candidates answer on the Question Paper. No Additional Materials are required.

READ THESE INSTRUCTIONS FIRST Write your Centre number, index number, name and class in the spaces provided at the top of this page. Write in dark blue or black pen. You may use a soft pencil for any diagrams, graphs or rough working. Do not use staples, paper clips, highlighters, glue or correction fluid. Section A Answer all questions. Section B Answer any two questions. You are advised to spend about one hour on each section. Write your answers in the spaces provided in this booklet. At the end of the examination, enter the Section B questions you have answered in the grid below. The number of marks is given in brackets [ ] at the end of each question or part question.

For Examiner’s Use

1 / 10

2 / 10

3 / 10

Section A

4 / 10

/20

Section B /20

Total /80

This booklet consists of 23 printed pages.



2

Data

speed of light in free space, c = 3.00 x 108 m s-1

permeability of free space, µo = 4π x 10-7 H m-1

permittivity of free space, εo = 8.85 x 10-12 Fm-1

(1 / (36 π)) x 10-9 Fm-1

elementary charge, e = 1.60 x 10-19 C

the 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

Formulae

uniformly accelerated motion, s = ut + ½at2

v2 = u

2 + 2as



gravitational potential, φ =

Gm

r−−−−

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

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

= ( )22

xxo

−± ω

mean kinetic energy of a molecule of an ideal gas E =

3

2kT

resistors in series, R = R1 + R2 + …

resistors in parallel, 1/R = 1/R1 + 1/R2 + …

electric potential, V = Q / 4πεor

alternating current/voltage, x = xo sin ωt

transmission coefficient, T = exp(-2kd)

where k =

(((( ))))2

2

8 m U E

h

π −−−−

radioactive decay, x = xo exp (-λt)

decay constant λ =

21

693.0

t



4

SECTION A

Answer all the questions in this section.

1 (a) Define simple harmonic motion.

[2]

(b) The set up in Fig. 1 is used to demonstrate forced oscillation.

A paper card and pin are taped to the top end of a flexible rod B, which is pivoted at its lower end such that it can only oscillate in a vertical plane. A pair of magnets can slide along rod B.

A heavy pendulum P is attached to rod A which is pivoted at a fixed axle. The position of the heavy pendulum can be adjusted along rod A.

Fig. 1

(i) State, with a reason, whether B or P is being forced to oscillate.

[2]



5

(ii) Suggest the effect of the following changes on the oscillations of rod B.

1. Turning the paper card by 90° about a vertical axis.

2. Moving the pair of magnets higher.

3. Increasing the number of rubber bands.

[3]

(iii) During the experiment, the frequency Pf of oscillation of the heavy pendulum

P is kept constant while the frequency Bf of oscillation of rod B is adjusted in

steps. After each adjustment on rod B, its amplitude A is noted when the oscillation becomes steady. Sketch two labelled graphs to show the variation of A with

Bf for

1. one rubber band, and

2. two rubber bands.

[Assume light damping is present.]

[3]

A

f B



6

2 (a) Distinguish between resistance and resistivity of a conductor.

[2]

(b) A cell of e.m.f. 2.50 V and internal resistance R is connected to two uniform resistive wires in series as shown in Fig. 2.1. The wires are made of the same material but have different lengths and diameters. Wire AB is 50.0 cm long and has a diameter d, whereas wire BC is 30.0 cm long and has a diameter 0.30 d. The ammeter and connecting wires are assumed to have no resistance.

Fig. 2.1

Show that AB

BC

R

R= 0.150

[2]

R

2.50 V

A B C

A



7

(c) A battery of e.m.f. 2.00 V and internal resistance r is connected across wire BC in parallel with another resistor of resistance r as shown in Fig 2.2. The galvanometer shows no deflection when the jockey J is at the midpoint of wire BC.

Fig 2.2

(i) Show that VBC = 2.00 V [1]

(ii) Determine the internal resistance R of the 2.50 V cell if the ammeter shows a reading of 0.400 A.

R = Ω [3]

(d) Suggest and explain whether your answer in part (c)(ii) is an over-estimate or under-estimate if the ammeter is not ideal.

[2]

R

2.50 V

A B C

r

r

2.00 V

A

J



8

3 (a) Fig. 3.1 shows the essential energy levels of an atom in the production of laser light.

(i) Identify each of the energy levels, E1, E2 and E3, with ‘metastable state’, ‘ground state’ and ‘excited state’.

E1

E2

E3 [2]

(ii) By drawing arrows on Fig. 3.1 to represent the movement of electrons, explain the production of laser light.

[3]

E3

E2

E1

Fig. 3.1



9

(iii) In a ruby laser, electrons may reside at the metastable state for up to 3.0 ms. Calculate the minimum uncertainty in the frequency of the photon emitted during the production of laser light.

Minimum uncertainty in frequency = Hz [2]

(b) Fig. 3.2 shows a typical X-ray spectrum produced by an X-ray tube where electrons are accelerated through a constant accelerating potential towards a metal target.

(i) Account for the value λmin.

[1]

(ii) Explain the changes in the X-ray spectrum when the accelerating potential is decreased. Sketch the new spectrum on Fig. 3.2.

[2]

minλ

0

Intensity

Kβ

Kα

Wavelength

Fig. 3.2



10

4 A cyclotron is a device used to accelerate ions to very high speeds. Fig. 4 shows a diagram of a cyclotron viewed from above. It is composed of two hollow, semi-circular electrodes called “Dees”. The “Dees” are encased inside a vacuum chamber and exposed to a perpendicular uniform magnetic field. An ion source lies in between the “Dees” at point A. An alternating voltage supply is connected across the “Dees”.

During operation, the voltage supply produces an alternating electric field in the small gap between the “Dees”. This is to ensure that the ions are accelerated each time they cross the gap. On entering the “Dees”, the uniform magnetic field causes the ions to move in a circular path. As the ions speed up, they travel in ever larger circles within the “Dees”. Once the ions reach a sufficiently large speed, they exit through an outlet in one of the “Dees” which is aimed at a target.

Fig. 4

At any time when an ion of mass m and charge q accelerates across the small gap, the potential difference between the “Dees” is V. The ion then travels in a circular path in the “Dees” where a uniform magnetic field of flux density B is applied perpendicularly.



11

(a)

Show that the time T for the ion to complete one revolution is

2 m

Bq

π.

Ignore relativistic effects.

[2]

(b) A helium nucleus of mass 6.68 x 10-27 kg and charge 2e is accelerated in the cyclotron by applying an alternating potential difference of 450 V across the “Dees”. The magnetic flux density through the “Dees” is 0.850 T.

(i) Calculate the time T to complete one revolution for the helium nucleus.

T = s [2]

(ii) Determine the frequency f of the alternating voltage supply so that the helium nucleus is accelerated everytime it crosses the gap between the “Dees”.

f = Hz [2]



12

(iii) State an expression for the gain in kinetic energy of the helium nucleus after one revolution in terms of e and V.

Gain in kinetic energy = [1]

(iv) Hence, determine the speed v of the helium nucleus after five revolutions.

v = m s-1 [3]



13

SECTION B

Answer two questions in this section.

5 A ball of mass m = 3.00 kg is released from rest at a height h = 0.500 m on a frictionless

incline as shown in Fig 5.1. The incline, which makes an angle θ = 30.0o to the horizontal, is fastened to an immovable table of height H = 2.00 m.

Fig. 5.1

(a) Determine the contact force between the incline and the ball, after the ball is released.

Contact force = N [2]

(b) Determine the acceleration of the ball as it slides down the incline.

Acceleration = m s-2 [2]

m

h

H

R

θ



14

(c) Hence, or otherwise, show that the speed of the ball as it leaves the incline is 3.13 m s-1. [2]

(d) Calculate the horizontal range R of the ball.

Horizontal range = m [4]

(e) The estimated normal contact force acting on the ball upon hitting the floor is shown in Fig. 5.2. Assume that the floor is frictionless.

Fig. 5.2

Normal contact force / N

Time / s 0 0.200

360



15

(i) Determine the impulse delivered to the ball in the vertical direction.

Vertical component of impulse = N s [2]

(ii) Hence, determine the vertical speed of the ball at the instant it rebounds from the floor.

Vertical speed of rebound = m s-1 [4]

(iii) State and explain whether this is an elastic or inelastic collision. Describe the energy changes during the collision.

[4]



16

6 (a) State two conditions for observable interference of two waves.

[2]

(b) In an aircraft landing system, it is important to guide the aircraft along the centre-line of the runway prior to landing. In a simple landing system, rows of light guides are lined along the runway to help guide the pilot.

The minimum power of light that can be detected by the human eye of area 0.50 cm2 is about 2.5 × 10-11 W. If an aircraft is 12 km away from the runway, find the required power of one light guide such that it is observable by the pilot. Assume that the light guide is a point source and that there are no energy losses.

Power = W [3]



17

(c) In another type of landing system, aircrafts are guided using interference of radio waves. Fig. 6.1 shows two radio wave emitters P and Q positioned 50 m apart at the end of the runway. The two emitters emit radio waves of frequency f1 in phase.

The aircraft can be guided by searching for the strong signal radiated along the lines of constructive interference, also known as anti-nodal lines. To ensure that the aircraft is along the centre-line of the runway, the aircraft needs to “lock on” to the central anti-nodal line.

(i) Suggest why radio waves are used instead of waves of shorter wavelengths (e.g. microwaves, etc.).

[2]

(ii) Explain why the entire centre-line will always be an anti-nodal line.

[2]

Top view (figure not to scale)

P

Q

Anti-nodal lines

Fig. 6.1

runway



18

(d) One particular aircraft at a vertical height of 480 m strays off the centre-line as shown in Fig. 6.2. Fig. 6.3 shows the radio wave signals from P and Q detected by the aircraft in this position.

(i) The source of signal B is emitter P. Using Fig. 6.3, explain why this is so.

[1]

(ii) State the phase difference between signals A and B.

Phase difference = rad [1]

Signal B

Fig. 6.3

time

Signal detected by aircraft

Signal A

50 m

4800 m

180 m

480 m

(diagram not to scale)

P

Q Fig. 6.2



19

(iii) Hence determine the frequency f1 of the radio wave used.

f1 = Hz [4]

(e) As an additional precaution to prevent the aircraft from “locking on” to the wrong anti-nodal line, the emitters can simultaneously emit another radio wave of a different frequency f2. However, for this precaution to work, the ratio of the two

frequencies 1

2

f

f should not be an integer ratio (e.g.

1

2,

2

3,

4

3, etc.).

(i) Explain how this precaution can prevent the aircraft from “locking on” to the wrong anti-nodal line.

[1]

(ii) Explain why the ratio of the two frequencies should not be an integer ratio.

[2]



20

(f) Suggest one advantage and one disadvantage of the wave-interference system over the light guide system in guiding aircrafts to land safely.

Advantage:

[1]

Disadvantage:

[1]



21

7 (a) Define binding energy.

[1]

(b) A minimum energy Q is required to remove a neutron from a helium-4 nuclide to form a helium-3 nuclide. The following data is given:

Binding energy per nucleon of helium-4 nuclide = 6.8465 MeV

Binding energy per nucleon of helium-3 nuclide = 2.2666 MeV

Mass of neutron = 1.0087 u

1 u = 931.494 MeV

(i) Write the nuclear equation for this reaction.

[1]

(ii) Calculate Q.

Q = MeV [3]

(iii) Hence, calculate the difference in mass between the helium-3 and helium-4 nuclides.

Difference in mass = u [3]



22

(iv) With reference to the above process, explain why the mass difference is less than the mass of a neutron.

[1]

(c) Helium-2 is a hypothetical isotope of helium which consists of two protons and no neutrons. It has negative binding energy.

(i) Explain the implication of the italicized terms on helium-2.

[1]

(ii) Suggest a reason for this.

[1]

(d) A radioactive source contains a mixture of nuclides 32

15P and 35

16S . The half-life of 35

16S is 6.14 times that of 32

15P . At time t = 0 s, 90% of the total activity from this

source comes from the 32

15P nuclides.

(i) Define half-life.

[1]

(ii) If the number of 32

15P nuclides is N at time t = 0 s, determine the number of 35

16S nuclides in the source in terms of N.

Number of 35

16S nuclides = [3]



23

(iii) Calculate the time elapsed for 90% of the total activity to come from the 35

16S nuclides, given that the half-life of 32

15P is 14.3 days.

Time elapsed = days [4]

(iv) Suggest a possible use for 32

15P , which is a beta-emitter with a half-life of

14.3 days.

[1]

END OF PAPER



2010H2Physics RI

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