CS (Main) Exam:2015 PHYSICS I P a p e r I


SECTION A
Answer all the following questions 10x5=50

Write down precisely the conservation theorems for energy, linear
momentum and angular momentum of a particle with their
mathematical forms! 10

Prove mathematically that the addition of any velocity of a particle to the velocity of light in free space merely reproduces the velocity of light in free space only. 10

How does one obtain the angular velocity of the Earth about the North Pole with respect to a fixed star as 7-292 x 1(T5 sec-1 Explain your method of calculating the above value. 10

A convex lens of focal length 20 cm is placed after a slit of width 0*5 mm. o If a plane wave of wavelength 5000 A falls normally on the slit, calculate the separation between the second minima on either side of the central maximum. 10

What is the role of an optical resonator in a laser Why does one prefer curved mirrors instead of plane mirrors in designing an optical
resonator 10

Q2. Find out the angle between the reflected and refracted rays when a parallel beam of light is incident on a dielectric surface at an angle equal to the Brewster’s angle. Explain how do you use this concept to produce linearly polarized light. 10+10=20

Using Poiseuille’s formula, show that the volume of a liquid of viscosity coefficient r passing per second through a series of two capillary tubes of lengths 11 and having radii and obtained as
where p is the effective pressure difference across the series. 15

Show that the moment of inertia of a circular disc of mass M and radius R about an axis passing through its centre and perpendicular to its plane is ^MR2. 15

Q3. Draw a neat diagram to explain the scattering of an incident beam of particles by a centre of force. 10

Show that the differential scattering cross-section can be expressed as
ds

sin 0 d0
where s is the impact parameter and 0 is the scattering angle. 15

Show that the rest mass energy of an electron is 0*51 MeV (use the standard values of the physical parameters). 10

Find out the phase and group velocities of a radio wave of frequency V2 cop in the ionosphere (as a dielectric medium) of refractive index n
go?
1 -r—. Here, « p is the ionospheric plasma frequency. 15

Q4. Define coefficients of viscosity and kinematic viscosity of a fluid. What are Poise and Stokes 10

Write down Poiseuille’s formula and mention its limitations in analyzing the flow of a liquid through a capillary tube. 10

Using matrix method, find out the equivalent focal length for a
combination of two thin lenses of focal lengths fi and f2 separated by a
distance a. 10

Using the concept of Einstein’s A and B coefficients for a two-level
atomic system under thermal equilibrium, determine the ratio of the
number of atoms per unit volume in the two levels experiencing
spontaneous and stimulated emission. How does the principle of
population inversion lead to the gain mechanism in the active medium of the laser? 10+10=20


SECTION B

Q5. Answer all the following questions 10x5=50

Under one-dimensional configuration, the charge density is given by where pQ is a constant charge density. If the electric field 5

E 0 at x 0 and potential V 0 at x determine V and E 10

A conducting sphere of radius 5 cm has a total charge Of 12 nC uniformly distribu-—t^ed on its surface in free space. Determine the displacement vector D on its surface and outside at a distance r from the centre of the sphere. 10

A series RLC circuit has a resistance of 100 Q. and an impedance of 210 Q.. If this circuit is connected to an a.c. source with an r.m.s. voltage of 220 how much is the average power dissipated in the circuit 10

Two spheres A and B having same temperature T are kept in the
surroundings of temperature TQ. Consider T TQ. The spheres are made of same material but have different radii rA and r^. Using
Stefan Boltzmann distribution, determine which of these will lose
heat by radiation faster. 10

A Van der Waals gas undergoes Joule-Kelvin expansion with a pressure drop of 50 atm. If its initial temperature is 300°K, determine its final temperature. (Given Van der Waals constant a 0*136 Pa m6 mol-1, b 36-5 x 10-6 m3 mol"1, Cp 30 J K"1 mol"1, R 8-3 J K"1 moH) 10

Q6. Derive the equation that represents Poynting’s theorem. What is its physical significance 20

A radio station transmits electromagnetic waves isotropically with an average power of 200 kW. Determine the average magnitude of the
maximum electric field at a distance of 5 km from it. 15

The vapour pressure of an organic substance is 50 x 103 Pa at 40°C. Its normal boiling point is 80°C. If the substance in vapour phase can be treated like an ideal gas, find the latent heat of vaporization of the substance. 15

Q7. A plane electromagnetic wave propagating along z direction is incident normally on the boundary at z 0 between medium A and medium B 0). Determine the reflection coefficient and
transmission coefficient for the wave. 20

A series RLC circuit has R 2 Q. The energy stored in the circuit
decreases by per period of oscillation. Its natural undamped
frequency is 2 kHz. Determine the values of inductor L and the quality
factor. 15

Using, Planck’s radiation law, deduce Wien’s displacement law. How does this law enable one to estimate the surface temperature of the Sun or a star 15

Q8. In the circuit given below, find the values of currents I2 and I.

What are the characteristic features of Rayleigh scattering A very thin monochromatic beam of light is incident on a particle. Suggest a simple experimental method to ascertain whether the scattering by the particle is of Rayleigh type. 20

For a Van der Waals gas, write down the equation of state. Determine the coefficient of critical expansion p. 15