This document contains an unsolved physics exam from 1991 containing 7 multiple choice questions and 7 fill in the blank questions. The multiple choice questions cover topics like collisions, oscillations, electric and magnetic fields, capacitors, and circuits. The fill in the blank questions require calculating values like distances, times, fractions, thicknesses, radii, and circuit connections. The document provides the questions and diagrams but no answers.

1. IIT JEE –Past papersPHYSICS- UNSOLVED PAPER - 1991

2. SECTION – ISingle Correct Answer TypeIn each part of this question, a statement is followed by four alternatives. In each part, one or more alternative(s) is (are) correct. Select the correct alternative(s) in each case and write down the corresponding letter(s) a, b, c, d in your answer book against the sub-question number. In your answers, the sequence of the sub-questions should be the same as in the question paper. For each sub-question, marks will be awarded only if the correct and only correct choice(s) is/are written.

3. 01ProblemA uniform bar of length 6 a and mass 8m lies on a smooth horizontal table. Two point masses m and 2m moving in the same horizontal plane with speeds 2v and v, respectively, strike the bar(as shown in Fig. 1991.1) and stick to the bar after collision. Denoting angular velocity (about the centre of mass), total energy and centre of mass velocity by , E and Vc respectively, we have after collisiona.b.c.d.

4. Problem02Two identical straight wires are stretched so as to produce 6 beats per second when vibrating simultaneously, On changing the tension slightly in one of them, the beat frequency remains unchanged. Denoting by T1,T2 the higher and the lower initial tensions in the strings, it could be said that while making the above changes in tensionT2 was decreasedT2 was increasedT1 was increasedT1 was decreased

5. Problem03A particle of charge +q and mass m moving under the influence of a uniform electric filed and a uniform magnetic filed follows a trajectory from P to Q as shown in Fig. 1992.2 The shown in Fig. 1992,2. The velocities at P and Q are . Which of 1the following statement(s) is/are correct? a. b. Rate of work done by the electric field at P is Rate of work done by the electric field at P is zero Rate of work done by both the fields at Q is zero.

6. Problem04A parallel plate capacitor of plate area A and plate separation d is charged to potential K is then inserted between the plates of the electric field between the plates (after the slab is inserted), and work done on the system, in question, in the process of inserting the slab, then a. b. c. d.

7. Problem05A micro ammeter has a resistance of 100 and a full scale range of 50 It can be used as a voltmeter or as a voltmeter or as a higher range ammeter provided a resistance is added to it. Pick the correct range and resistance combination(s). 50 V range with 10k resistance in series.10 V range with 200 k resistance in series.5 m A range with 1 resistance in parallel.10 m A range with 1 resistance in parallel.

8. SECTION – IIFill in the blanksBlank(s) to be filled appear in each of the following statements. Write, in your answer book, the sub-question number and in front of it write down your answer corresponding to each blank strictly in the order in which it appears in the statement.

9. 01ProblemThe slab of a material of refractive index 2 shown in Fig. 1991.3 has a curved surface APB of radius of curvature 10 cm and a plane surface CD. On the left of APB is air and on the right of CD is water with refractive indices as given in the figure. An object O is placed at a distance of 15 cm from the pole P as shown. The distance of the final image of O from P, as viewed from the left is_______________________

10. Problem02A solid copper sphere (density and specific heat capacity c) of radius r at an initial temperature 200 K is suspended inside a chamber whose walls are at almost 0 K. The time required for the temperature of the sphere to drop to 100 K is _____________

11. Problem03A piece of metal floats on mercury. The coefficients of volume expansion of the metal and mercury are and respectively. If the temperatures of both mercury and the metal are increased by an amount the fraction of the volume of the metal submerged in mercury changes by the factor __________________

12. Problem04A point source of heat of power P is placed at the center of a spherical shell of mean radius R. The material of the shell has thermal conductivity K. If the temperature difference between the outer and inner surface of the shell is to exceed T, the thickness of the shell should not be less than_______________.

13. Problem05The Bohr radius of the fifth electron of phosphorus atom (atomic number = 15) acting as a doping in silicon (relative dielectric constant = 12 ) is __________________Å

14. Problem06For the given circuit shown in Fig. 1991.4 to act as full wave rectifier, the ac input should be connected across ____________ and ____________ and the de output would appear across ____________ and ____________

15. Problem07A thin rod of length f/3 is placed along the optic axis of a concave mirror of focal length f such that its image which is real and elongated, just touches the rod. The magnification is _______________

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