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Preliminary Examination 2009 [Turn Over]

Name: _____________________________ Class: 08___________ PHYSICS 9745/01 Higher 2 Paper 1 3rd September 2009 1 hr 15 min

Additional Materials: Multiple Choice Answer Sheet 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. Shade in soft pencil. Do not use staples, paper clips, highlighters, glue or correction fluid. Write your name and class on the Answer Sheet in the spaces provided. There are forty questions on 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 separate Answer Sheet provided. Each correct answer will score one mark. A mark will not be deducted for a wrong answer. Total marks: 40

(This question paper consists of xx printed pages)

JURONG JUNIOR COLLEGE Preliminary Examination 2009

2 Data speed of light in free space, c = 3.00 × 108 m s-1

permeability of free space, μo = 4π × 10−7 H m−1

permittivity of free space, εo = 8.85 × 10−12 F m−1 = (1/(36π)) × 10−9 F m−1

elementary charge, e = 1.60 × 10−19 C

the Planck constant, h = 6.63 × 10−34 J s

unified atomic mass constant, u = 1.66 × 10−27 kg

rest mass of electron, me = 9.11 × 10−31 kg

rest mass of proton, mp = 1.67 × 10−27 kg

molar gas constant, R = 8.31 J K−1 mol−1

the Avogadro constant, NA = 6.02 × 1023 mol−1

the Boltzmann constant, k = 1.38 × 10−23 J K−1

gravitational constant, G = 6.67 × 10−11 N m2 kg−2

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

Formulae

uniformly accelerated motion, s = ut + 21 at 2 v2 = u2 + 2as

work done on/by a gas, W = p ΔV

hydrostatic pressure, p = ρgh

Gmgravitational potential, φ = −

r

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

velocity of particle in s.h.m., v = vo cos ωt v = ω± −2 2( ) ox x

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

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

electric potential, V = π o

Qε r4

alternating current / voltage, x = xo sin ωt

transmission coefficient, T = exp(-2kd)

where k = 2

2

)m U Eh

π −8 (

radioactive decay, x = xo exp(−λt)

decay constant, λ = 0.693t 12


3 1. Which of the following is not a reasonable estimate for the following physical quantities? A The power of an electric iron is 1 kW. B The momentum of a tennis ball served by a professional tennis player is 4 Ns. C The weight of a man on Moon is 100 N. D The kinetic energy of a double-decker bus moving smoothly along an expressway

is 50 kJ. Ans: D

A: within usual electric iron power specification, reasonable. B: about 80 g ball served at about 50 m s-1, reasonable. C: weight of man on Earth about 600 N meaning mass about 61 kg, reasonable. D: assuming mass of bus 10000 kg, speed is about 3 m s-1, not reasonable.

2. A tennis ball of mass 80 g moving horizontally at 4.0 m s-1 due north strikes a wall and

bounces off at 3.0 m s-1 due west. Determine its change in momentum. A 0.080 N s northwest B 0.40 N s north 37° west C 0.40 N s south 37° west D 0.56 N s southwest Ans: C

=+=Δ 22 )0.4()0.3(v 5.0 m s-1

== −

0.40.3tan 1θ 37°

Δv is 5.0 m s-1 south 37° west. Hence Δp = mΔv = (0.08)(5.0) = 0.40 N s south 37° west.

3. A parachutist falls vertically with a uniform speed of 3 m s-1. When he is 50 m from the

ground, he drops a coin. What is the time taken for the coin to reach the ground? A 2.1 s B 2.9 s C 3.5 s D 5.0 s Ans: B

( ) ( ).

2.9

2150 3 t 9 81 t2

t s

= +

=

4. Which of the following pairs of forces is not a valid example of action and reaction to

which Newton's Third Law of motion applies? A The weight of a satellite in orbit around the Earth and the attractive force on the

Earth's centre of mass due to the satellite. B The forces of repulsion experienced by two parallel wires carrying currents in

opposite directions. C The forces of attraction felt by two gas molecules passing near to each other. D The weight of an object resting on the table and the force acting on the object due

to the table supporting it. Ans: D

5. A light spring has a mass of 0.20 kg suspended from its lower end. A second mass of

θ Δv

3.0 m s-1

4.0 m s-1


4

0.10 kg is suspended from the first mass by a thread. The arrangement is allowed to come into static equilibrium. At the instant when the thread is cut, what is the upward acceleration of the 0.20 kg mass?

A 3.3 m s-2 B 4.9 m s-2 C 9.8 m s-2 D 20 m s-2 Ans: B

At equilibrium, T = 0.2g + 0.1g = 0.3g When the thread is cut, Resultant force = ma (upwards) 0.3g – 0.2g = 0.2a a = 4.9 m s-2

6. A particle X moving with kinetic energy E and momentum p makes a head-on collision

with an identical particle Y which is initially at rest but free to move. After the collision, the two particles stick together and move off with a common speed. Which of the following correctly represents the kinetic energy of the particle X and the system as a whole, and the magnitude of the momentum of X and the system as a whole, after this collision?

kinetic energy momentum

of X of system of X of system A 0 0 0 0 B 0 E 0 p

C E4

E2

p4

p2

D E4

E2

p2

p

Ans: D By COM, mu + 0 = 2mv v = ½ u System: Total p = 2mv = 2m (½ u) = mu = p Total KE = ½ (2m)(v2) = ½ (2m) (½u)2 = ½ (½ mu2) = ½ E X: p = mv = m (½ u) = ½ p KE = ½ mv2 = ½ (m) (½u)2 = ¼ (½ m u2) = ¼ E

7. Two masses X and Y of density 3800 kg m-3 and 4000 kg m-3 respectively, are balanced

horizontally by a beam balance inside a water tank as shown in the diagram below. (Size of masses are not drawn to scale and density of water is 1000 kg m-3)

Beam balance

Y X

Tap


5

Y

Subsequently, all the water in the tank is drained away through the tap. Which of the following diagrams shows the possible positions of the masses and beam balance?

A

B

C

D

Ans: C In water:

X X Y Y

X X f X Y Y f Y

X X f XY Y f

W U W UV g V g V g V g

V ( ) V ( )

− = −ρ −ρ = ρ −ρ

ρ −ρ = ρ −ρ

Since X Y XV Vρ < ρ → >

f X f Y

X Y

V g V gW W

→ρ > ρ→ >

8. A stone of mass 0.60 kg is projected horizontally at a speed of 4.0 m s-1 from the top of

a wall, 5.0 m above the surrounding ground. Just before it hits the ground, its speed is 7.0 m s-1. The energy it lost in falling through the air is

A 9.9 J B 15 J C 20 J D 29 J Ans: C

Taking ground as datum, At launch: Total Energy = KE + GPE = ½ (0.60)(4.0)2 + (0.60)(9.81)(5.0) = 34.2 J Arrival at ground:

Y

X X Y

Y X

Y

X


6

Total Energy = KE + GPE = ½ (0.60)(7.0)2 + 0 = 14.7 J Energy loss through air = Energy at launch – Energy at ground = 34.2 – 14.7 = 19.5 J

9. An object tied to the end of a light inextensible string of length 25 cm is swung in a

vertical circle as shown below.

Determine the minimum speed of the object in order that the string remains straight

throughout the motion. A 1.6 m s-1 B 2.2 m s-1 C 2.5 m s-1 D 3.1 m s-1 Ans: A

At the highest point of the vertical circular motion, the minimum speed occurs when the tension just decreases to zero. The weight of object supplies the centripetal force.

6.1)81.9)(25.0(2

===→= rgvr

mvmg m s-1

10. Consider the objects X and Y, each of mass 8000 kg and 0.25 m apart, as shown

below, where ABP forms an equilateral triangle.

Determine the resultant gravitational field strength at point P due to objects X and Y. A 3.7 ×10-6 N kg-1 B 8.5 ×10-6 N kg-1 C 1.5 ×10-5 N kg-1 D 1.7 ×10-5 N kg-1 Ans: C

0.25 m

Y (8000 kg)

X (8000 kg) 60° 60°

P

25 cm


7

52

11

2 105.160sin)25.0(

)8000)(1067.6(260sin2 −−

×=°×

=°=r

GMg N kg-1

11. P and Q are two points above Earth’s surface and at respective distances d and 2d

from the centre of the Earth as shown below.

The gravitational potential at P is −800 kJ kg-1. An object of mass 2 kg is moved from P

to Q. Determine the work done on the object. A −800 kJ B −400 kJ C +400 kJ D +800 kJ Ans: D

Gravitational potential at Q is -400 kJ kg-1. Work done = mΔφ = (2)[(-400)-(-800)](103) = 800 kJ

12. Which of the following could be the temperature on a hot afternoon in Singapore?

A 23 °C B 33 K C 293 K D 306 K Ans: D

A: 23 °C is too cool to be the temperature on a hot afternoon. B: 33 K is very low temperature, more than 200 °C below ice point. C: 293 K is about 20 °C, too cool to be the temperature on a hot afternoon. D: 306 K is about 33 °C, possibly the temperature on a hot afternoon.

13. Ice of mass m at 0 °C is added to water of mass m at 100 °C. Assuming no heat loss to

the environment and given that the latent heat of fusion of ice and the specific heat capacity of water are 3.3 × 105 J kg-1 and 4.2 × 103 J kg-1 K-1 respectively, determine the final temperature of the mixture.

A 0 °C B 11 °C C 21 °C D 79 °C Ans: B

Let the final temperature be θ. Heat gained by ice = heat lost by water ml + mcθ = mc(100-θ) (3.3 × 105) + (4.2 × 103)θ = (4.2 × 103)(100-θ) θ = 11 °C

Q

P

d

d

Earth


8 14. An ideal gas is contained in two spherical containers X and Y of volume 2V and V

respectively, connected by a hollow tube of negligible volume. The containers X and Y are maintained at temperatures 2T and T respectively. The setup is shown in the diagram below.

Determine the ratio number of moles of gas in container Xnumber of moles of gas in container Y

.

A 0.25 B 1.00 C 2.00 D 4.00 Ans: B

Container X: X X XX Y X X X

X

n RT n RTp V n RT pV V

= → = =

Container Y: 22

Y Y Y YY Y Y Y Y

Y

n RT n R T n RTp V n RT pV V V

= → = = =

Since X Yp p= , X Yn n= , 1X

Y

nn

= .

15. Two monatomic gases X and Y are in thermal equilibrium in a mixture. The molecules

of Y have double the mass of the molecules of X. The root-mean-square (r.m.s.) speed of the molecules of gas Y is 700 m s-1. Determine the r.m.s. speed of the molecules of gas X.

A 350 m s-1 B 700 m s-1 C 990 m s-1 D 1400 m s-1 Ans: C

Thermal equilibrium ⇒ same mean translational k.e.

222

22

212

21 =→==→=

Y

X

X

Y

Y

XYYXX c

cmm

cccmcm

990)700)(2())(2( ===→ YX cc m s-1

16. The least distance between two points along a progressive wave with a phase difference of 1.2 radians is 2.0 m. Given that the frequency of the wave is 200 Hz, determine the speed of the wave.

A 76.4 m s-1 B 240 m s-1 C 667 m s-1 D 2100 m s-1 Ans: D

V T

2V

2T

X Y


9

5.100.22

2.1=→= λ

λπm

2100)5.10)(200( === λfv m s-1

17. A sound wave with an amplitude of 0.20 mm has an intensity of 3.0 W m-2 incident normally on a surface. What is the intensity of a sound wave of the same frequency but with an amplitude of 0.40 mm?

A 3.0 W m-2 B 4.2 W m-2 C 6.0 W m-2 D 12 W m-2 Ans: D

2AI ∝kAI =

2

11 and 222 kAI =

12)4)(0.3()20.040.0)(0.3()( 22

1

2122

1

2kAI 2

1

2 ====→=A

IIkAI

A W mm-2

18. Which of the following is false for a system in resonance?

A The driving frequency coincides with the natural frequency of the system. B The amplitude of oscillation of the system is maximum. C When damping is increased, the peak of the frequency response graph shifts to

the right. D When damping is increased, the amplitude of oscillation of the system decreases. Ans: C

19.

The displacement vs distance graph for two sinusoidal waves having different wavelength and amplitude is shown below.

The result of superposing these two waves is A

B


10

C

D

Ans: C.

By applying Principle of Superposition at selected distance x.

20. A diffraction grating with 5000 lines per cm is illuminated normally by white light. The

wavelengths for red and violet light are taken to be 650 nm and 400 nm respectively. Which of the following statement is correct?

A The central fringe is dark. B The angular displacement of the third-order violet from the central fringe is

sin-1 0.6. C The red end of the second-order spectrum is closer to the central fringe than the

violet end of the first-order spectrum. D The second-order fringe of red coincides with the third-order fringe for violet. Ans: B.

Using d sin θ = n with λmperlines105000

m12×

=d , n = 3 and = 400 × 10-9 m λ

A. Central fringe is always bright (white light in this case) since path difference is zero. C. Using the above equation, θ (40.5°) for second-order red > θ (11.5°) for first-order violet. D. Since d is constant, we need only compare n λ for second-order red and third-order violet. (2)(650) is not equal to (3)(400), hence their respective θs are not equal and they do not coincide.

21. Which one of the following statements is correct?

A When an electron, travelling in a vacuum, enters a uniform electric field E directed

at right angles to its path, it is deflected in the direction opposite to E into a parabolic path.

B When an electron is brought from a point of higher electric potential to a point of lower electric potential, the work done on the charge is negative.

C The electric force acting on an electron varies with positions in an electric field between two large parallel plates with a potential difference.

D The electric potential energy of an electron is higher nearer to a positive point charge than a negative point charge.

Ans : A (A) is correct


11

(B) is wrong. An electron is brought from a point of higher electric potential to a lower electric potential. The work done on the charge is positive. (C) is wrong. The electric force acting on an electron is constant at different positions in an electric field between two large parallel plates with a potential difference. (D) is wrong. The electric potential energy of an electron is lower nearer to a positive point charge than a negative point charge.

22. Two horizontal metal plates, each of length 100 mm, are separated by a distance D.

The potential difference between the two plates is 2.0 V, as shown below.

If an electron situated between the two plates experiences an electric force of

6.4 × 10−16 N upwards, the direction of the electric field and the distance between the two plates, D is

A Upwards, 0.25 mm B Upwards, 0.50 mm C Downwards, 0.25 mm D Downwards, 0.50 mm Ans: D

mmmF

VqdqdVEqF 5.00005.0

104.6106.12)( 16

19

==×××

==⇒== −

−

23. The current of a horizontal beam of alpha particles is 5.0 μA. Given that these alpha particles travel at a speed of 2.0 x 105 m s-1, what is the average number of alpha particles found in one centimetre length of this horizontal beam?

A 7.8 x 105 B 1.6 x 106 C 1.6 x 1013 D 9.8 x 1013 Ans: B

electron

100 mm

2.0 V

556

108.7)

100.201.0)(105(

×=××

==⇒==

−

ItnnqQI 19106.12 ×× −qtt

24. A cell of e.m.f. 5.0 V and negligible internal resistance is connected to four similar

resistors and a variable resistor T, as shown.


12

Resistance of each resistor is 1.0 kΩ and resistance of T is 5.0 kΩ. What is the reading of the ideal voltmeter?

A 0 V B 2.0 V C 3.0 V D 5.0 V Ans: C

VreadingRR eff

eff

3)5(2

312

3

23

21

611

=+

=⇒=⇒+=

25. A sinusoidal alternating current has period T. The r.m.s value of the current in a resistor is I and the mean power dissipated in the resistor is P. Which statement is correct?

A The frequency is 2πT

.

B The maximum power dissipated in the resistor is

12

P .

C The peak current is

2I

.

D The r.m.s voltage is

IP

.

Ans: D

(A) is wrong as frequency = T1

.

(B) is wrong as maximum power = 2P (C) is wrong as peak current = I2 (D) is correct.

26. Half-wave rectification of an alternating sinusoidal voltage gives the waveform as shown

below.

T

5.0 V

V


13

The r.m.s value of this rectified voltage is 100 V. The peak voltage is A 50 V B 71 V C 141 V D 200 V

Ans: D

20022

==⇒= rmsoo

rms VVVV V

27. Two particles A and B emitted by a radioactive source at M, made tracks in a cloud

chamber within a magnetic field which was directed into the paper, as illustrated below.

Careful measurements showed that both tracks were circular, the radius of track A

being half that of track B. Which of the following statements is certainly true?

A The speed of B is half that of A. B The mass of B is half that of A. C The charge of B is half that of A. D Both A and B are negative charges. Ans: D

2mvr

= Bqv r = mvBq

The mass, velocity and charge of the particles are unknown, Ans A, B, C are uncertain. Both particles curve to the right, indicating that they are both negative charges.

28. Suppose a particle P is projected in a uniform field which can be magnetic, electric or

gravitational as shown below;

V/ V

t/ s


14

For the particle to move in the plane of the paper in a circular path as indicated, the conditions would have to be:

Particle Field

A positively charged electric B positively charged magnetic C Uncharged gravitational D There are no conditions which could produce such a motion.

Ans: D

Circular path is only found in magnetic field. The magnetic force is always perpendicular to the field, so the path cannot in the plane of the paper.

29. The diagram below shows a rectangular wire PQRS moving at a constant velocity v into

a magnetic field of flux density B. The length of RQ is y. B is directed at an angle θ to the plane of the rectangular wire.

At the instant shown above, RQ is a distance x from the edge of the magnetic field. The magnetic flux associated with the rectangular wire, φ, and the induced e.m.f. between R and Q, ε are:

Flux φ Induced e.m.f. ε

A Bxy sin θ Byv sin θ B Byv sin θ Bxy sin θ C Bxy sin θ Bxv sin θ D Bxy cos θ Byv cos θ

Ans: A

Flux φ = BA (where B is normal to A) φ = Bxy sin θ Induced emf ε = BLv (where v is perpendicular to B) ε = Byv sin θ

30. When a coil is rotated in a magnetic field, the induced e.m.f. E varies with time as

shown below.

y


15

Which of the following graphs, drawn to the same scale, would be obtained if the speed of rotation of the coil is halved?

A E

t

B E t

C E t

D E t

Ans: B

When ω is halved, the maximum emf is halved and period is doubled.

31. The maximum kinetic energy Ek of emitted electrons is measured in photoelectric experiments using light of particular intensity. Which of the following is a possible graph showing how Ek varies with the wavelength λ of the light?

A

B

C

D

Ans: A

= −λkhcE

E

t

λ

Ek

λ

Ek

Ek Ek

λ λ

φ


16

Ploting Ek against λ will yield a graph of option A.

32. The electron energy levels in a certain atom are represented by the given diagram below. If the atom in the ground state E1 is bombarded with an electron of energy 4.0 eV, which is/are possible transition/s that can take place?

A Only E1 to E3 B Only E1 to E2 or E1 to E3 C Only E1 to E2 or E1 to E3 or E1 to E4 D Any transition between the four energy levels is possible. Ans: B

As it is bombardment by electrons, any transition from the ground state to a higher energy level that requires energy less than or equal to the energy of the electron is possible.

33. What is the effect of doubling the accelerating voltage across an X-ray tube?

A The X- rays are more likely to be less penetrating. B The minimum wavelength of the X-rays is doubled. C The intensity of the X-ray beam is increased. D The wavelengths of the characteristics lines at the peaks of the spectrum are

halved. Ans: C

Intensity of X-rays will increase when the kinetic energies of the incoming electrons are higher. A: X ray should be more penetrating if the voltage is higher as the intensity is higher. B: Minimum wavelength should be halved. D: No change in the wavelengths of the peaks because it depends on the metal used.

34. An electron in a potential well, has a wave function Ψ as shown.

At which points (A, B, C and D) would the probability of finding the electron the highest?

Ans :C

E3 E4 -7.6 eV

-8.0 eV

E2 -9.4 eV

E1 -12.0 eV

Ψ

A C DB x0


17

The value of lΨl2 gives the probability of finding the electron at a point. The magnitude is the largest at C.

35. Which of the following statements about semiconductor is correct?

A Semiconductors have a gap of a few eVs between their valence and conduction

bands. B Their resistivity is normally lower than that of insulators. C Electrical conduction in a p-type semiconductor is due to the transfer of protons. D An intrinsic semiconductor is produced by doping Group V atoms called donors. Ans: B

By definition. A: The gap should be about 1 eV only. C: It is due to the transfer of holes. D: Intrinsic semiconductors have no donor or acceptor.

36. In a p–n junction, free electrons near the junction in the n–type material diffuse across

the junction into the p–type material. Diffusion occurs because A the concentration of free electrons in n–type material is large and in p–type

material is small. B the n-type material is negatively charged while the p-type material is positively

charged. C the electric field created across the depletion layer cause electrons to diffuse

continuously across the p–n junction. D of different thermal agitation of atoms in the n–type and p–type material Ans: A

Diffusion is the spontaneous net movement of particles from an area of high concentration to an area of low concentration.

37. The radioactivity decay processes for an unstable nuclide P are as follows:

α β β α P → Q → R → S → T

Which of the following is not correct? A The proton number of S exceeds that of Q. B Q and S have the same nucleon number. C P and S are isotopes. D Q and T have the same mass number. Ans: D

4 42 2

A AZ ZP Q α−

−→ + leads to 4 42 1

A AZ ZQ R 0

1β− −− − −→ + leads to

4 4A AR S 011Z Z β− −→ +− −

4 leads to 4 8A AS T2 2Z Z α− −→ +− A, B and C are true.

38. A neutron, a proton and a helium nucleus ( ) have masses of 1.009u, 1.008u and

4.003u respectively.

42He

Assuming that protons and neutrons can fuse to form helium, the binding energy per nucleon of a helium nucleus is


18


A 0.0031u B 0.0078u C 0.0310u D 0.4965u Ans: B

mass defect of = (2)(1.009) + (2)(1.008) − 4.003 = 0.031u 42He

which is equivalent to its binding energy; binding energy per nucleon of is equivalent to 0.031u / 4 = 0.00775u 4

2He

39. Given that the mass of 14 is 14.003974u and that the sum of the masses of and is 14.011179u, it would be reasonable to suppose that the nuclear reaction

7N 11H

136C

11H + → 13

6C147N

A can only take place if there is a net supply of energy. B could not take place at all. C must involve the emission of a further uncharged particle. D will result in the emission of energy. Ans: D

The mass of the product is less than that of the reactants, so A and B are not reasonable. The nucleon number and proton number are conserved, so C is not reasonable.

40. A particular medical application requires a radioactive source with an activity of 3.90 × 103 Bq at the start of the treatment. The nuclide selected has a half-life of 1.80 × 105 s. It is prepared at a Radio-isotope Centre one week (6.05 × 105 s) before the treatment is due to commence. The activity of the source at the time of preparation should be

A 3.90 × 103 Bq B 4.79 × 103 Bq C 4.01 × 104 Bq D 8.02 × 104 Bq Ans: C

n =1/ 2

tt

=5

5

6.05 101.80 10

××

= 3.36

o

AA

= 12

n⎛ ⎞⎜ ⎟⎝ ⎠

33.90 10

oA× =

3.3612

⎛ ⎞⎜ ⎟⎝ ⎠

Ao = 4.01 × 104 Bq

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