IIT-JEE-Physics-Mains–2001

MAINS 

Time : two hours                                                               Max. Marks : 100 
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General Instructions : 
1. There are ten questions in this paper. Attempt all Questions. 
2. Answer each question starting on a new page. The corresponding question number must be written in the left margin. Answer all the parts of a question at one place only. 
3. Use only Arabic numerals (0, 1, 2 ………….9) in answering the questions irrespective of the language in which your answer. 
4. Use of logarithmic tables is not permitted. 
5. Use of calculator is not permitted. 
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1. An ice cube of mass 0.1 Kg at 00C is placed in an isolated container which is at 2270C. The specific heat S of the container varies with temperature T according to the empirical S = A + BT, where A = 100 cal/Kg-K and B = 2 × 10–2 cal/K2. If the final temperature of the container is 270C, determine the mass of the container. 
(Latent heat of fusion for water = 8 × 104 cal/Kg, 
Specific heat of water = 103 cal/Kg-K). 

2. A small ball of mass 2 × 103 Kg having a charge of 1 µ C is suspended by a string of length 0.8 m. Another identical ball having the same charge is kept at the point of suspension. Determine the minimum horizontal velocity which should be imparted to the lower ball so that it can make complete revolution. 

3. An inductor of inductance L = 400 mH and resistors of resistances R1 = 2 W and R2 = 2 W are connected to a battery of e.m.f. E = 12 V as shown in the figure. The internal resistance of the battery is negligible. The switch S is closed at time t = 0. 

             

What is the potential drop across L as a function of time? After the steady state is reached, the switch is opened. What is the direction and the magnitude of current through R1 as a function of time? 

4. A 5 m long cylindrical steel wire with radius 2 × 10–3 m is suspended vertically from a rigid support and carries a bob of mass 100 Kg at the other end. If the bob gets snapped, calculate the change in temperature of the wire ignoring radiation losses. 
(For the steel wire : Young’s modulus = 2.1 × 1011 Pa; 
Density = 7860 Kg/m3; Specific heat = 420 J/Kg-K) 

5. The refraction indices of the crown glass for blue and red light are 1.51 and 1.49 respectively and those of the flint glass are 1.77 and 1.73 respectively. An isosceles prism of angle 6o is made of crown glass. A beam of white light is incident at a small angle on the prism. The other flint glass isosceles prism is combined with the crown glass prism such that there is no deviation of the incident light. Determine the angle of the flint glass prism. Calculate the net dispersion of the combined system. 

6. In a nuclear reactor 235U undergoes fission liberating 200 MeV of energy. The reactor has a 10% efficiency and produces 1000 MW power. If the reactor is to function for 10 years, find the total mass of uranium required. 

7. A nucleus at rest undergoes a decay emitting an a-particle of de-Broglie wavelength, l = 5.76 × 10–15 m. If the mass of the daughter nucleus is 223.610 a.m.u. and that of the a-particle is 4.002 a.m.u., determine the total kinetic energy in the final state. Hence, obtain the mass of the parent nucleus in a.m.u. 
(1 a.m.u. = 931.470 MeV/c2) 

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