Physics - Main Examination - 2002

Time allowed: Three hours Maximum marks: 300

Instructions

Each question is printed both in Hindi and in English.

Answers must be written in the medium specified in the Admission Certificate issued to you, which must be stated clearly on the cover of the answer book in the space provided for the purpose. No marks will be given for the answers written in a medium other than that specified in the Admission Certificate.

Candidates should attempt Questions 1 and 5 which are compulsory, and any three of the remaining questions selecting at least one question from each section.

Assume suitable data if considered necessary and indicate the same clearly.

All questions carry equal marks.

**PAPER I**

**SECTION A.**

1. Answer any three of the following:

(a) Using the rocket equation and its integral
find the final velocity of a single stage rocket. Given that (i) the velocity of
the escaping gas is 2500 m/s, (ii) the rate of loss of mass is . (where m_{0}) is the initial mass and 0.27
m_{0} is the final mass).

(b) Two spaceships are moving at a velocity of 0.9 c relative to the Earth in opposite directions. What is the speed of one spaceship relative to the other? (c = velocity of light)

(c) A wave is represented by , velocity v, frequency f and the direction of propagation. If it interferes with another was given

)
and separated in time by t=10^{-6} s.

6. (b) A Geiger tube consists of a wire 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

(i) the capacitance of the system, and

(ii) the charge per unit length of the wire when the potential difference between the wire and the cylinder is 1.2 kV.

6. (c) A series LCR circuit with L = 2 H, C = 2 F and R = 20 ohm is powered by a source of 100 volts and variable frequency. Find

(i) the resonance frequency,
f_{o},

(ii) the value of Q

(iii) the width of resonance f and

(iv) the maximum current at resonance.

7. (a) Why did Maxwell have to introduce the idea of displacement current? Derive the wave equation from Maxwell's laws. Obtain Fresnel's formula for reflection and transmission coefficients of the electric vector when it is perpendicular to the plane of incidence.

7. (b) What are vector and scalar potentials for the electromagnetic field? Are they unique? Explain what are Coulomb's and Lorentz gauges. Derive the electromagnetic wave equation in Lorentz gauge and show that it is equivalent to Maxwell's equation.

8. (a) Discuss the phenomenon of Bose-Einstein condensation. Obtain the expression for the condensation temperature. Briefly comment on observation of Bose-Einstein condensate.

8. (b) A bulb filament is constructed from a tungsten wire of length 2 cm and diameter 50

Instructions

Each question is printed both in Hindi and in English.

Answers must be written in the medium specified in the Admission Certificate issued to you, which must be stated clearly on the cover of the answer book in the space provided for the purpose. No marks will be given for the answers written in a medium other than that specified in the Admission Certificate.

Candidates should attempt ** Questions 1 and 5 which are compulsory**, and

Assume suitable data if considered necessary and indicate the same clearly. Some constants are given below.

All questions carry equal marks.

1

1

1

1

1

1

1