Section A [15 marks]Answer all questions in this section.

1. The displacement x of a body of mass 0.02 kg in simple harmonic motion is given by the equation

x = 5.0 x 10-3 sin (6πt)

where x is in metres and t in seconds. Which of the following is true about the maximum velocity and the maximum restitution force?

Maximum velocity Maximum restitution force

A 1.5 x 10-3 m s-1 9.0 x 10-5 N

B 1.5 x 10-2 m s-1 9.0 x 10-4 N

C 3.0 x 10-2 m s-1 3.6 x 10-3 N

D 9.4 x 10-2 m s-1 3.6 x 10-2 N

2. A spring-mass system experiences critical damping. Which of the following graphs represents the variation of the displacement s with time t of the motion of the mass?

3. A progressive wave is represented by the equation

y = a sin (bt - cx).

The speed of the progressive wave is

A. ab

B. ac

C.bc

D.cb

4. A pipe is open at both ends. If the length of the pipe is l, the wavelength of the fundamental tone is slightly

A. more than l B. more than 2l

C. less than l D. less than 2l

5. A point source produces a- sound at the rate of 120 W uniformly in all directions. What is the intensity level of the sound at a distance of 2.0 m from the source?[Take the threshold of hearing = 10-12 W m-2]

A. 30 dB

B. 124 dB

C. 130 dB

D. 141 dB

6. Which of the following statements is true of electromagnetic waves?

A. Electromagnetic waves are the transverse type of mechanical waves.

B. Electromagnetic waves are made up of electric and magnetic vibrations in parallel directions.

C. The electric and magnetic vibrations of the electromagnetic waves are represented by the equations E = E0 sin (ωt - kx) and B = B0 cos (ωt - kx) respectively.

D. The speed c of the electromagnetic waves in free space can be expressed in terms of free space permittivity ɛ0 and free space permeability µ0 by the

equation c=1

√ɛ0 µ0

7. Which of the following is the most probable frequency of the yellow light which is produced from sodium vapour light?

A. 5 x 1010 Hz

B. 5 x 1012 Hz

C. 5 x 1014 Hz

D. 5 x 1016 Hz

8. The diagram below shows two thin lenses L1 and L2 which are placed coaxially at a distance 30cm apart. Each lens has a focal length of 40 cm.

If the incident rays to are parallel, the final image which is produced after the rays pass through lenses L1 and L2 is

A. real and located between L1 and L2

B. virtual and located between L1 and L2

C. virtual and located at the left side of L1

D. real and located at the right side of L2

9. The diagram below shows the arrangement of Young’s double-slit experiment. S is the monochromatic light source of wavelength A. The centre of the interference pattern which is produced on the screen is located at O with OS being perpendicular to the two slits S1 and S2. P is the location of the second dark band.

Which of the following is true about the phase difference between the waves from S1 and S2, and the optical path difference between S1P and S2P?

10. When a lens is 18.0 cm from an object, an upright image, which is one-third the size of the object is produced. What is the focal length of the lens?

A. 4.5 cmB. 6.0 cmC. -9.0 cmD. -18.0 cm

11. Which of the following is NOT true for a spontaneous nuclear reaction?A. Radioactive decays of radio isotopes are spontaneous nuclear reactions.B. Spontaneous nuclear reactions occur naturally.C. Spontaneous nuclear reactions can occur at a higher rate at higher

temperature.D. Spontaneous nuclear reactions are not affected by changes in pressure.

12. The graph below shows the variation of the binding energy per nucleon with nucleon number for some naturally occurring nuclides.

What is the binding energy of nuclide Gd64156 ?

A. 8.30 x 10-11 JB. 9.00 x 10-11 JC. 2.03 x 10-10 JD. 2.19 x 10-10 J

13. Which of the following can be inferred from mass defect?A. The loss in mass has changed into the binding energy.B. The conservation of mass does not apply for nuclear process.C. Energy is required to separate the individual constituent nucleons of a

nucleus.D. The rest mass energy of a nucleus is more than the total rest mass energy of

its constituent nucleons.

14. The characteristic lines in an X-ray spectrum is caused byA. deceleration of the energetic incident electrons while they approach the

target.B. collision of energetic incident electrons with the target atoms. C. release of energy when the target atoms undergo ionization.D. transitions of electrons between innermost shells of the target atom.

15. Nanoscience is generally known as the study on systems withA. sizes less than one nanometer.B. sizes from one to one hundred nanometers.C. mass of one to one hundred nanograms.D. interaction time of one to one hundred nanoseconds.

Section B [15 marks]Answer all questions in this section.

16. A form of progressive wave which has a frequency of 800 Hz and a speed of 350 m s-1 can be stated in the form of the following equation.

y = A sin (ωt - kx).

(a) Calculate the value of(i) ω,

[2 mark]

(ii) k.

[3 marks]

(b) What is the distance between the two positions which gives the phase difference of π rad?

[2 marks]

17. The diagram below shows two pieces of Polaroids, P and Q, which are arranged such that the polarisation axes make an angle d between one another. A plane unpolarised incident light beam of intensity I0 is applied to Polaroid P. The amplitude of light wave between Polaroids P

and Q is A, and the amplitude after Polaroid Q is A2

(a) State, in terms of I0, the intensity I1 of the light beam between Polaroids P and Q.

[2 mark]

(b) Calculate the angle θ between the polarisation axis of Polaroid P and that of Polaroid Q.

[3 marks]

(c) Deduce the intensity I2 of the light beam after Polaroid Q in terms of I0.

[3 marks]

Section C [30 marks]Answer any two questions in this section.

18.a. Define simple harmonic motion.

[2 marks]b. A mass performing simple harmonic motion is expressed by displacement,

x=5.0 cos (2 π t + π7) from equilibrium position, where x is in metres and t in

seconds. Determine:i. the maximum velocity. [2 marks]

ii. the maximum acceleration. [2 marks]iii. the frequency of the motion. [2 marks]

c. The bob of a simple pendulum is displaced and then released.i. Show that the time when the kinetic energy of the system equals to one

fifth of its potential energy, is approximately 1.80T.[4 marks]

ii. Deduce the subsequent time when the kinetic energy of the system equals to one fifth of its potential energy again.

[3 marks]

19.a.

i. Define diffraction of waves. [2 marks]ii. By using the Huygen’s principle, explain the single slit diffraction

phenomenon. [2 marks]iii. Sketch the variation of the intensity of light across the single slit

diffraction pattern with the angle of diffraction. [2 marks]b.

i. By using a ray diagram, show that the destructive interference of a single slit diffraction is given by:

sinθ=mλa

where θ is the diffraction angle, λ the wavelength, a the width of the slit and m an integer.

[4 marks]ii. State and explain the changes in the interference pattern, when:

1. the width of the slit is twice the initial value2. the slit is illuminated with a light of higher frequency.

[3 marks]

iii. A laser beam of wavelength 633 nm is directed perpendicularly at a narrow slit of width 0.080 mm. The light is diffracted and falls on a screen placed 1.2 m away. Determine the width of the central maximum which appeared on the screen. [2 marks]

3

20.a. What is meant by half-life and decay constant of a radioactive substance?

[2 marks]b. Radioisotopes are used widely in various industries.

i. Define radioisotopes. [1 mark]ii. A sample of radioisotopes has the initial activity of 300 Bq. The half

life of the radioisotope is 337.5 s. After a duration of 45 minutes, what is the percentage of reduction from the initial value of activity that has taken place?

[3 marks]c. Give three examples of the use of radioisotopes in heavy industries.

[3 marks]d. Radioisotopes are also playing an important role in medical field. A medical

specialist uses 1.79 µg of iodine-131 to treat thyroid disorder. Iodine-131 has half-life of 8.0 days. Calculate:

i. the initial number of nuclei present. [3 marks]ii. the initial activity. [3 marks]

ANSWER

1. D2. D3. C4. B5. B6. D7. C8. D9. C10. A11. A12. A13. A14. D15. A