P-1 PHYSICS

B.Sc., DEGREE EXAMINATION (PHYSICS-PAPER-I)

Paper I-MECHANICS. WAVES AND OSCILLATIONS

Time : Three hours                                              Maximum: 100 marks

SECTION A - (4 x 15 = 60 marks)

Answer ALL questions.

1 (a) What are elastic and inelastic collisions? Give examples. Derive expressions for   

        final velocities of two bodies after a one-dimensional elastic collision between    

        them.

or

  (b) Derive Euler's equations of motion for a rigid body. Explain the working of a  

       gyroscope.

2 (a) State and prove Kepler's laws of planetary motion.

or

   (b) Describe the Michelson-Morley experiment and explain the physical significance of  

        the negative result.

3 (a) Define simple harmonic motion and explain its characteristics. Derive expressions  

        for the frequency and energy of a simple harmonic oscillator.

Or

   (b) State and explain Fourier theorem. How do you use it to analyze a square wave.

4 (a) What is a transverse wave? Obtain the equation of the velocity of a transverse

        wave in a stretched string. Mention the laws of transverse vibrations of the strings.

Or

   (b)Write an essay on the production, and applications of ultrasonic waves.

SECTION B - (5 x 4 = 20 marks)

Answer any FIVE of the following

5. Explain Scalar and Vector fields.

6. Explain the principle of working of a rocket

7. Explain time dilation.

8. Show that central forces are conservative in nature.

9.  What are Lissajous' figures?

10. Define quality factor.

11. Explain fundamental frequency, overtones and harmonics.

12. Compare longitudinal and transverse vibrations in a bar.

SECTION C - (5 x 4 = 20 marks)

Answer any FIVE of the following

13. If r is the position vector of a point, prove that curl r =0.

14. If the mean distance of Mars from the Sun is 1.524 times that of the Earth. find the period of revolution of Mars about the sun.

15. A top of mass 1 kg and rotational inertia5 x 10¹¹ kg-m ² is spinning at 30 rotations per second about an axis making an angle of 30° with the vertical. Its centre of mass is 4 cm from the origin. Find its angular speed of precession.

16. The Young's modulus of elasticity of steel is 2x10¹¹ N/m² and its rigidity modulus is   8 x 10¹⁰ N/m ² find its Poisson's ratio and bulk modulus of elasticity.

17. Find velocity with which a body should be moving such that it gets rest mass doubled.

18. The displacement equation of a particle describing simple harmonic motion is           x =0.001 sin 50 π (t + 0.007) meter. Calculate the amplitude, time period, maximum velocity and initial phase for the particle.

19. If the frequency of a stretched string of length 1 m is 256 Hz, find the frequency of the string of half the length under identical conditions.

20. A piezo-electric crystal with thickness 3 x 10^-3 m has density 3.5 x10³ kg/m.lf its Young's modulus is 8 X 10¹⁰ N/m ², what is fundamental frequency?