Time Allowed: 3 Hours M=imumMarks: 300
Candidates should attempt Questton 1 and 5 which are compulsory, and any three of the remammg questtons selecttngat least one questtonfrom each &Jctton All questtons carry equal marks

Attempt any three of the following
(20x3=60)
A block of mass is attached to an ideal massless spring of force constant is at rest on a smooth horizontal floor A second block of mass 2 is, moving with an initial velocity strikes the free end of the spring. The collisiOn lS one dimensiOnal and elastic
Calculate the maximum compreSSion of the spring
What are the velocities of the block long time after the collisiOn?
An observer sees two bodies A and B haVing equal rest mass approach each other with equal but opposite velocities 4c15. To a second observe S" the body A lS at rest What us the velocity of the body B as seen by observe What are the kinetic energies of the body B in the frames of and
Two transverse harmonic waves, each of amplitude 5mm, wavelength travelling in opposite directions along a stretched string fixed at both ends 1m and speed 3 m/s are Obtain an expresSion for the standing WeNe Produced. Locate the position at the nodes and antinodes
Two thin convex lenses of focal length 0.2 in and 0.1 in are located 0 1m apart on the axlS of symmetry. An object of height 0 1m lS placed at a distance of 0 2 in from the first lens. Find by the matrix method, the position and the height 0 f the Image
Write the Euler's equations for the rotational motion of a rigid body with one point fixed, under the action of torque N. Apply these equations to discuss the rotational motion of a symmetrical top in the absence of any force other than the reaction at the fixed point
An Ideal massless spring of force constant k has a mass m attached to one of its ends, the other and being fixed to a ragid support. The spring iS horizontal floor, A reSiStive force proportional to the velocity v acts on the mass. Assuming the damping to be light, obtain the frequency of oscillation. When m 0 1 kg and k 10 ItlS found that the frequency of oscillation lS .J1T2 times the frequency In the absence of damping. Calculate the value of the constant b
Write the Lagrange's equation for a system of particles which iS acted upon by Conservative forces What iS a cyclic co ordinate? Show that the generalized momentum conjugate to a cyclic co ordinate lS conserved
(b)How does Doppler effect of light of relativlStic phySics qualitatively differ from its non-relativistic analogue? Calculate the Doppler shift in the frequency 0f a photon travelling along the y-aXlS WIth respect to an observer moving along the X-axiS with a constant speed v

Explain the phenomenon 0f pulse dispersion in a step index optical fibre
What iS holography? Describe the experimental set up for Gabors on-line holographic recording What are the limitations of Gabors experiments? How these were over come by Leith and Upatneiks?
Obtain an expressiOn for the intensity of light in the Fraunhofer diffraction pattern due to a Circular aperture. WhatlS pattern? Explain with a neat diagram
Explain the phenomenon 0f self focusing of laser beams
SEcTION B
Answer any three of the folloWing
(20x3=60)
A cylinder oF length L and radius b has it S axiS coincident with Z-axlS The electric held in the region iS E lOOk Find the electric flux through the top Circular end the bottom circular end the closed surface of the cylinder the curved wall of the cylinder

<img images/1103-2-a.jpg'> A bridge network with reSiStance, capacitance and inductance lS given in the above figure. Show that the conditions for balancing the bridge are independent of the frequency of applied voltage
Earth reCelves 1 of radiant energy from the Sun. Assuming Sun to be a spherical black body of radius 7 x 108m and Earth-sun distance to be 1 5 x 10um, Calculate the surface temperature of Sun. (Stefan-Boltzmenn constant [sigma 5.67x 10-3
100 particles at a temperature T and distributed among three energy levels Eo kT and Eo 2kT WhatlS the total energy of the system?
ConSider an infinite grounded conducting plane If a point charge is held at a distanced d from the plane, compute by method of Images, the electric potential above the plane and the induced charges on the conductor
Define Poynting vector and explain its Significance The electric field vector for an electromagnetic field travelling in nvacuum Is given by E-Eo cos(kz-(wt)i Calculate the Poynting vector for the wave and show that ItS magnitude lS equal to the energy density of the wave time the velocity of light
<img images/1103-6c.jpg'> A parallel LC CircuitlS operated at a frequency OJ, which lS less than the resonant frequency OJo of the LC Circuit Explain whether the reactance is inductive or capacitative
What iS Laplace equation? Determine the average electric potential over a spherical surface, due to a point charge q placed at a distance r from the centre of the sphere Assume r to be greater than the radius of the sphere
A plane wave of frequency omega, which to two linear dielectric media It has a normal incidence at the interface 0f the media Giving appropriate for the intensities 0f reflected and transmitted rays

Two bodies A and B have the same mass in each and are made of the same material With speCific heat C per unit mass. A lS at a temperature T and B is at a temperature 4T What W111 be the entropy change of the universe when the bodies are brought into diathermic contact with each other?

Describe the Otto cycle and obtain an expressiOn for the effiCiency of the cycle, Show that the effiCiency lS lower than that of a Carnot cycle operating between the highest and the lowest temperature 0f Otto cycle
Define Fermi energy. For an ideal Fermi gas of N particles at absolute zero temperature, show that
the total energy OflS 3/5 NEF, where EFlS the Fermi energy