S7 MOCK EXAMINATION 04-05

PHYSICS PAPER 1

Name

Class
Class No.
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Question / Answer Book

Time allowed: 3 hours

Total number of pages: 16

(including this page)

GENERAL INSTRUCTIONS

  1. You should keep silent throughout the test/examination.
  1. Do not start writing until you are instructed to do so.
  1. All equipment such as watches and calculators must not make any sound during the test/examination.
  1. Do not write anything or erase your answers after the ‘Time is up’ announcement. Stay at your seats and keep quiet until you are told to leave.
  1. Any violation may cause disqualification or mark penalty.

INSTRUCTIONS ON THIS PAPER

  1. This paper carries 120 marks
  1. Write your name, class and class number in the spaces provided on this cover.
  1. You should answer ALL questions in this paper.
  1. Write your answers in the spaces provided in this question/answer book. In calculations you should show all the main steps in your working.
  1. Assume:velocity of light in air = m s-1

acceleration due to gravity = 10 m s-2

Do not turn over this page until you are told to do so

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  1. A boy holds the end, O, of a rubber cord from which hangs a solid metal ball.

Figure 1.1Figure 1.2

(a)When the ball is still, as in Figure 1.1, the rubber stretches. Draw a diagram showing the forces acting on the ball. What do you know about these forces? (2 marks)

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(b)In Figure 1.2 the boy whirls the ball in a horizontal circle, keeping his hand still. Draw a diagram showing the forces acting on the ball in the position A. Explain carefully why the rubber cord stretches more in the situation of Figure 1.2 than in that of Figure 1.1. (2 marks)

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(c)Explain why each of the forces in the situation of Figure 1.2 does no work as the ball rotates.

(2 marks)

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(d)If the rubber cord breaks when the ball is at A, state clearly the direction in which the ball will move, giving reason for your answer. (2 marks)

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(e)At A the ball is 1.25 m above the ground. Calculate the time it will take to reach the ground after the cord breaks. (The time is the same as if the ball were to fall vertically from rest.) (2 marks)

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(f)If at the moment the cord breaks the ball is moving at 1.5 m/s, what will be the horizontal distance from A when it reaches the ground? (2 marks)

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(a)A cylinder of mass m and radius r rolls down an incline plane which makes an angle θ to the horizontal. The diagram shows only the forces acting on a cylinder along the inclined plane, viz. the component of the weight down the plane and the static friction f between the cylinder and the plane. The moment of inertia of the cylinder about its axis is 1/2 mr2.

(i)State the relationship between the linear acceleration a of the cylinder and the angular acceleration α about its axis, if the cylinder rolls without slipping. (1 mark)

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(ii)Show that the friction force is given by f = 1/3 mg sin θ.(3 marks)

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(iii)The plane must be rough enough for rolling to take place.Find an expression for the coefficient of static friction between the plane and the cylinder for the cylinder to roll down the plane without slipping. (2 marks)

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(b)A yo-yo has a moment of inertia of 1.2 × 10-4 kgm2 and a mass of 0.15 kg. Its axle radius is 5.0 mm and its string is 1.0 m long. The yo-yo rolls from rest down to the end of the string.

(i)Determine the total kinetic energy of the yo-yo when it reaches the bottom.(1 mark)

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(ii)Hence, calculate its maximum speed v.(3 marks)

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(iii)From the consideration of the forces acting on the yo-yo, determine its acceleration.(3 marks)

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(iv)Hence, verify your answer in (b) (ii).(2 marks)

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3.Figure 3.1 shows a light spring fixed vertically to the ground at its lower end and with a small aluminum pan of negligible weight attached to its upper end. When a small block of mass 0.2 kg is placed on the pan, a compression of 4 cm is observed after the pan settles. Assume the spring obeys Hooke's law and damping can be neglected.

Figure 3.1

(a)Find the force constant (i.e. force per unit extension or compression) of the spring.(1 mark)

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(b)(i)If the block and the pan are pushed slightly upwards and released, calculate the period of oscillation of the system. (2 marks)

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(ii)Find the maximum amplitude of oscillation for which the block would not leave the pan.

(3 marks)

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(iii)Figure 3.2 shows the variation of kinetic energy of the block with its height about the ground. (The gravitational potential energy of the block is taken to be zero at the ground.

kinetic energy/J

Figure 3.2

height/m

00.040.080.12

(I)Find the amplitude of oscillation of the block.(1 mark)

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(II)If the total energy of the system remains constant at 0.17 J, find the maximum elastic potential energy stored in the spring. (2 marks)

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(c)The system is now brought to a planet with a greater gravitational field strength than that of the Earth. How would the answers to (b)(i) and (b)(ii) be affected? Explain briefly. (2 marks)

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4.Most of the colours in nature are due to selective absorption of light of different wavelengths by pigment,but a few are due to interference effects caused by a thin layer of transparent material.

(a)Suggest how you can tell whether the colour of an animal is due to selective absorption or interference effect. (2 marks)

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(b)Say whether the colour is monochromatic or not if it is resulted from (i) selective absorption and (ii) interference effect. (2 marks)

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(c)The "yellow eye" on the wing of a certain butterfly is due to constructive interference in a thin film which rests on another film of higher refractive index. What is the minimum thickness of such a film if its refractive index is 1.42 and the wavelength of yellow light in air is 580 nm? (2 marks)

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(d)Certain beetle has a set of parallel grooves on its back, 1200 nm apart. If white light is incident normally on this surface, what colour would you see looking at an angle of 36∘to the normal?

(2 marks)

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5.One mole of helium gas undergoes a cycle ABCA in which its pressure, P, and volume, V, are indicated in the P-V diagram in Figure 5.

P/105 Pa

0.6

Figure 50.3

0V/m3

0.50.8

Given:Universal gas constant = 8.31 J mol-1 K-1

Avogadro constant = mol-1

Assume that helium gas behaves as an ideal gas.

(a)(i)Find the temperature of the gas at state A.(2 marks)

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(ii)The average separation between helium atoms can be taken as the cube root of the average volume of space occupied by each atom. Estimate a value for this average separation at state A. (2 marks)

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(b)In an ideal gas, there are no intermolecular forces between molecules except during collisions. Is this ideal gas assumption justified for the helium gas? Explain briefly. (2 marks)

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(c)(i)Find the work done by the gas in going from (1) A to B, (2) B to C and (3) C to A.(3 marks)

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(ii)Find the internal energy of the gas at state A.(2 marks)

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(iii)Calculate the heat absorbed by the gas in going through the cycle ABCA.(2 marks)

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6.A thunder cloud with a large flat square base measuring 3000 m 3000 m passes over an area of level ground. Assuming the cloud carries a total charge of 4 C which is spread evenly over its base and is at a height of 0.5 km above the ground.

(Permittivity of free space F m-1)

(a)Estimate the potential of the cloud relative to the ground.(3 marks)

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(b)(i)What is the smallest charge a raindrop of radius 1 mm will carry if it does not fall under the action of gravity? (3 marks)

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(ii)If the breakdown strength of the air is approximately 3 MV m-1, determine whether it is likely that the drop in (b)(i) can carry such a charge. Explain your answer. (3 marks)

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(c)If the cloud discharges completely in a single lightning stroke last 10-3 s, calculate

(i)the mean discharge current, and

(ii) the energy released.(2 marks)

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7.In Figure 7.1, an a.c. signal generator of constant r.m.s. output voltage is connected in series with a resistor, R, of resistance 55Ω, a inductor, L, of inductance 270 mH and an ammeter, A. Both the signal generator and the ammeter have negligible impedance. Y1 and Y2 are connected to the two Y-inputs of a dual trace CRO while E is connected to its common earth connection. Figure 7.2 shows the stable trace pattern, y2, of the voltage across R and L shown on the CRO screen. The voltage gain and time base for y2 are 2.5 V cm-1 and 2.5 ms cm-1 respectively.

Figure 7.1Figure 7.2

(a)(i)What are the peak voltage and the frequency of the applied a.c. signal?(2 marks)

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(ii)Draw a phasor diagram to show the relationship between the applied a.c. voltage, the voltage across the inductor and the voltage across the resistor. (2 marks)

(iii)Find the phase angle between the applied a.c. voltage and the voltage across the resistor.

(2 marks)

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(iv)What is the peak voltage across the resistor?(2 marks)

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(v)Sketch on Figure 7.2 the trace pattern of the voltage across R, using the same time base setting of y2 but with a voltage gain of 1 V cm-1. (2 marks)

(b)A variable capacitor C, is added to the circuit in Figure 7.1 to form an RLC series circuit. When the capacitance of C is gradually decreased, the reading of the ammeter A increases to a maximum and then decreases.

(i)Explain why the ammeter reading attains a maximum.(2 marks)

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(ii)Find the value of the capacitance of C corresponding to the maximum ammeter reading.

(2 marks)

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8.A capacitor is stray if the intervening medium is conducting. In an experiment, a stray capacitor is formed by two parallel plates each of area 100 cm2 and separated by a layer of material of thickness 2.0 mm. The resistivity and the permittivity constant of the intervening material arem and F m-1 respectively.

(a)Find the capacitance C and resistance R of the parallel plate system.(3 marks)

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(b)Draw a diagram to show how the stray capacitor can be represented by an ideal capacitor C and a pure resistor R. (1 mark)

(c)

Figure 8

Figure 8 shows an experimental setup intended to charge the stray capacitor by keeping the current drawn from the 12 V cell constant. The variable resistor is initially set at 1.0 kΩand is adjusted continuously until its resistance is zero. Assume that the capacitor is initially uncharged and the internal resistances of the cell and the ammeter are negligible.

(i)What is the ammeter reading at the beginning?(1 mark)

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(ii)While the ammeter reading is kept at its initial value, the charge stored on the capacitor is increasing. When the stored charge is Q, find the rate at which charge is being stored in the plates in terms of Q. (3 marks)

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(iii)What are the current and the stored charge at the end of the experiment?(2 marks)

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(iv)Sketch a graph to show how the charge stored in the capacitor varies with time.(2 marks)

9.

Figure 9.1

(a)In an experiment with an illuminated photocell using caesium as the cathode, a small current is detected by the microammeter even when the anode is made slightly negative with respect to the cathode, using the circuit of Figure 9.1. Briefly account for this. (2 marks)

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(b)The current falls to zero only when the reverse p.d. across the tube reaches a value Vs, which varies with the frequency f of the radiation used to illuminate the cathode. Figure 9.2 shows the relationship between Vs and f.

Figure 9.2Vs/V

f /1014 Hz

(i)What is the relationship between Vs and f as predicted by Einstein's photoelectric theory?

(2 marks)

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(ii)What is the value of the threshold frequency for caesium?(1 mark)

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(iii)If the electronic charge is C, estimate a value for the Planck constant.(2 marks)

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(iv) Calculate the work function for caesium in electron-volts.(3 marks)

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(v)Sketch on Figure 9.2 the corresponding variation between Vs and f for a photocell whose cathode has a smaller work function than caesium. (2 marks)

10.

Figure 10

Figure 10 shows what happens to one unit of energy produced in the nuclear reactor of a nuclear power plant

(a)Suppose the electrical power output of this plant is 1066 MW, calculate

(i)the total power generated by the reactor,(1 mark)

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(ii)the power lost to the atmosphere.(1 mark)

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(b)The turbine is cooled by circulating water through it at the rate of 48 m3 s-1. Calculate the rise in temperature of the cooling water. (3 marks)

(Density of water = 103 kg m-3, specific heat capacity of water = 4200 J kg-1 K-1)

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(c)In the reactor, energy is produced by the fission of uranium 235 atoms,

235U + n 141Ba + 92Kr + 3n .

Masses of the above nuclides are : 235U = 235.0409 u, 141Ba = 140.9141 u, 92Kr = 91.9250u,

n = 1.0086 u. (1 u = kg)

Calculate the number of uranium atoms which undergo fission in 1s.(3 marks)

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(d)The nuclear plant is designed to produce power continuously for 10 years without refuelling. Estimate the mass of uranium 235 that will be consumed in this time, assuming that only the above reaction takes place. (Avogadro constant = mol-1) (2 marks)

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(e)In an emergency, explain how the reactor can be shut down immediately.(2 marks)

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END OF PAPER

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