PHYSICS paper 1

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

1. Answer any three of the folloWlng (20x3=60)

A parallel laser beam lS inCldent perpendicularly on a photographic plate An object lS placed at a distance a In front of the photo graphic plate. Discuss the recording from the plate .If the plate lS illununated by the same light, whatlS expected and why?

A star of the Size of our sun having a radius of 7 x km and having a mass 2 times as that of the sun lS rotating at a speed of one revolution 10 days. If the star undergoes a gravitational collapse to a neutron star of radius 10 kms, assuming that the star lS a unlfonn sphere at all times, calculate the rotation speed of the neutron star.The moment of mertia of solid about its diameter lS 2/5 where M and R are the mass and radius of the solid sphere respectively

The mass of muon at rest lS 207 where lS the electron rest mass (0.5 I I MeV). The mean life time at rest for muon lS 2.2 news. The life time of muon emerging from an accelerator lS measured in the laboratory as 6.9 s. Estimate the speed of these muons in the laboratory

A system with 2 independent coordinates Xl and has the following Larangian

alfa,beta,gama being constants. Obtain the Lagrangian equation 0f motion

Determine equation of trajectory for a particle under central force the magnitude of which lS given by
F=-A/r2+b/R3where A and B are positive constants
Obtain the equation 0f moti on 0f a particle moving relative to a rotating frame 0f reference Explain the term representing conohs force in this expreSSiOn

Define scaltenng cross-section A charged particle of mass m and charge lS scaltered by another charged partic! e 0 f charge at rest Deduce the expressiOn for the scaltenng ero ss-section

A person In a spaceship lS holding a rod of length of 0.5 the space ship lS ClUlSmg at a speed V parallel to the earths surface. What does the person In the space ship notice as the rodlS rotated from parallel to perpendicular to the sp ace ship s motion? What do es an observer on earth's surface notice?

Certain string has a linear mass density of 0 25 kgm-l and stretched With atensiOn of25 N One end lS giVen a smus01dal motion, Its frequency 5 Hz and amplitude 0.01 metre. If att the end has zero displacement and lS movmg along the positive Y direction, denve the wave speed, the wavelength and the wave equation of the wave m the string 20

The phase velocity in a material lS root g/k where k lS the propagation constant Prove that the group velo a ty will be half 0f the phase veloaty

4. Parallel rays fallon clrcul ar aperture of diameter 1 mm At a certain p0S1tion 0f the screen one gets a dark spot on an aXial point When the screen lS moved by 12.5 cm, one again gets a dark spot Determine y (wavelength)

Monochromatic light from a distance source of wavelength y falls on a double slit A glass plate of thickness t iS Inserted between one shi and the screen Calculate the intensity at the central point as the function of thickness t

Why does one getpolansed Fight from a Nicol's pnsm? How should one adjust the polariser and analyser, so that an intensity of the incident light lS reduced by a factor of 0.25?

SElmON B

5. Answer any three of the folloWlng (20x3=60)

What value of inductance has to be used so that a lamp with rating of200 volt and 10 Amperes lights the same way With 250 V source at 50 Hz
WhatlS gauge transfonnation? Define coulomb gauge. Denve the equation for vector potential under coulomb gauge
Calculate the mcrease m entropy when 1 kg Ice melts at zero degree centigrade The Latent heat of fusiOn 0f Ice lS 3.36 x 10-5Joules/kg (Assume that the melting lS an lSothennal reversible pro cess)
Calculate the electric field as a function of position due to a dipole whose potentiallS given by

The dipole is located at the ongln of the y axlS system

An inductance lS connected to 6 oh battery through areSlStance R WhatlS the steady state current the Circuit? Alter what time the ballery would be dehvenng one half its steady state current?
Explain the use 0f a parallel resonance Clfcuit as a ector CircUlt for current amplification
A conducting sphere of radius lS placed m a uniform electric field Eo USing the method of
images show that the potential function lS given by


7. Define scalar and vector potentials. Recast Maxwell's equations in terms of these potentials
Denve the energy continuity equation for electromagnetic WeNes using the poynting vector
From Planck's radiation law, denve Wien' s displacement law and Rayletgh Jean's law

8. Derive an expressiOn for the Max wellian distribution 0f velocities for the molecules of an ideal gas
Obtain vander waals' equation of state for real gases WhatlS the value of critical coefficient for an ideal gas? Show that the value of the critical coefficient for van der Waals' gas lS independent of the type of gas
How can one obtain a temperature and identify the elements in stellar bodies using Saba's thermal iorusation equation?