PHYSICS PAPER 1 2002

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

Answer any three of the folloWlng
USIng the rocket equation and its mtegral find the final velocity of a smgle stage rocket Given that the velocity of the escaping gaslS 2500 mis, the rate 0floss of mass lS. (where mol lS the llU tial mass and 0.27 mo lS the final mass)
Two spaceships are moving at avelocity of 0.9 c relative to the Earth m opposite directions WhatlS the speed of one spaceship relative to the other? velocity of light)
A wave lS represented by 10 cos(5x+25t). Find wavelength 1c, veloaty frequency f and the direction of propagation. If it Interferes with another was giVen by MEW 20cos(5x+25t+PIE/3), find the amplitude and the phase of the resultant wave. (All dimensiOns are in SI system)
Derive the expreSSiOn for resolving power of a diffraction grating with N Imes Calculate the maximum number of lines in the diffraction grating If it has to resolve the yellow lines of sodium (5890 nm and 589.6 running the first order

USIng the Lagrangian for the system of a planet and the Sun obtam the equation of motion to gel the equations forthe orbit Use them
Denve the relationship between the Impact parameter and the scallenng angle for the scattermg of an particle of charge +2e by a nucleus of charge +Ze. Calculate the Impact parameter for an angle of deflection of30' If the kinetic energy of the alphaparticlelS 6" 10-13 J

State Fennat's pnnaple. Apply it to get the laws of reflection from aplane surface

The phase velocity of the surface WeNe m aliqUld of surface tensiOn T and density p lS gIVen by

Show that the group vel ocity Ug 0f the surface wave lS gIVen by

An observer A sees two events at the same space point (delta x=delta y=delta and separated in time by delta I0-6 s. Another observer B sees them to be sep arated by delta t5 3xl 0-6 s What lS the sep aration in space of the two events as ob served by WhatlS the speed 0f B relative to A

How do you know that the lightlS a transverse weNe? WhatlS a quarter WeNe plate? How lS it constructed?

Discuss the Fresnel diffraction pattem fonned by a straight edge uSing the Comus splral
In an experiment using a Mlchelson interferometer, explain with the help of sUltable ray diagrams Why do we need extended source of light, Why do we gel Clfcular fringes, and Shifting of fringes mwards or outwards as we shift the movable nurror

SECTION B

5 Solve any three of the following

Calculate the electri c Ii eld for a point on the axlS of a uniforminng 0f a charge and radius a Show that the maXlmum value occur at x ±a/2
Show that the potential energy of a charge Q uniformly distributed throughout the sphere of radius R lS given by

Describe Carnot cycle and show that effiCIency is glven by

where the symbols have thelr usual mearung
Derive the Bose-Einsten distribution for an ldeal gas

6. Using Kirchoffs laws find currents in each branch of the ClrcUlt shown m the folloWlng diagram

A Gelgertube conSists ofawue a Wire of radius 0 2 mm and length 12 cm and a co aXial metallic cylinder of radius 1 5 cm and length 12 cm Find
the capaCItance ofthe system, and
the charge per unit length of the Wire when the potential difference between the Wlre and the cylinder is 12 kV (Assume the dielectric constant of the gas in the tube to be

A senes LCR clrcUltwith L 2 C 2 and 20 0" powered by a source of 100 volts and vanable frequency Find
the resonance frequency, £"
the value of Q
the Width of resonance M and
the maximum current at resonance

Why did Maxwell have to mlroduce the 1dea of displacement current? Denve the WeNe equahon from Maxwell's laws. Obtam Fresnel's fonnula for reflection and lransmlSSlon coeffic1ents of the el ectric vector when itlS perpendicul ar to the plane 0f inC1dence
What are vector and scalar potentials for the electromagnetic field? Are they ull1que? Explam what are Coulomb's and Lorentz gauges. Denve the electromagnetic WeNe equation 1n Lorentz gauge and show that itlS eqU1 valent to Maxwell's equation

8. Discuss the phenomenon 0f Bo se-Einstem condensation Obtam the expreSSiOn for the condensation temp erature. Bnefly conunent on observation 0f Bo se-Einstem condensate
A bulb filamentlS conshucted from atungsten Wlre of length 2 cm and diameter 50 m ItlS enclosed m a vacuum bulb What temperature does it reach when itlS operated at a power of I watt? Given
EmlSSlV1ty 0f tungsten" 0.4
Stefan's constant sigma= 5. 67x I 0. 8