2. SECTION – I Single Correct Answer Type In each part of this question, a statement is followed by four alternatives Of which one or more alternative(s) is(are) correct. Select the correct Alternative(s) and write down the corresponding letter(s) a, b, c, d in your Answer book against the sub-question number. In your answer, the sequence Of the sub-question should be the same as in the question paper. For each Sub-question, marks will be awarded only if all the correct alternatives, And no wrong alternatives, selected.
3. 01 Problem A particle P is sliding down a frictionless hemispherical boel. It passes the point A at t = 0. At this instant of time, the horizontal component of its velocity is v. A bead Q of the same mass as P is ejected from A at t = 0 along the horizontal string AB, with the speed v. Friction between the bead and the string may be neglected. Let tP and tQ be the respective time taken by P and Q to reach the point B. Then tP < tQ tP = tQ tP > tQ tP/tQ =
4. Problem 02 Two blocks A and B, each of mass m are connected by a massless spring of natural length L and spring constant K. The blocks are initially resting on a smooth horizontal floor with the spring at its natural length, as shown in Fig. 1993.2. A third identical block C, also of mass ra, moves on the floor with a speed v along the line joining A and B and collides with A. Then the kinetic energy of the A-B system, at maximum compression of the spring, is zero the kinetic energy of the A-B system, at maximum compression of the spring, is mv2/4 the maximum compression of the spring is the maximum compression of the spring is .
5. Problem 03 One end of a long metallic wire of length L is tied to the ceiling. The other end is tied to a mass less spring of spring constant K. A mass m hangs freely from the free end of the spring. The area of cross section and the Young's modulus of the wire are A and Y respectively. If the mass is slightly pulled down and released, it will oscillate with a time period T equal to a. b. c. d.
6. Problem 04 A particle of mass m moves on the Jt-axis as follows: it starts fromrest at t = 0 from the point x = 0, and comes to rest at t = 1 at thepoint x = 1. No other information is available about its motion atintermediate times (0 < t < 1). If denotes the instantaneous accelerationof the particle, then cannot remain positive for all t in the interval cannot exceed 2 at any point in its path must be 4 at some point or points in its path must change sign during the motion, but no other assertion can be made with the information given.
7. Problem 05 A solid sphere of uniform density and radius 4 units is located with its centre at the origin O of coordinates. Two spheres of equal radii 1 unit, with their centers at A (- 2, 0, 0) and B (2, 0, 0) respectively, are taken out of the solid leaving behind spherical cavities as shown 1 Fig. 1993.3. Then a. the gravitational force due to this object at the origin is zero.b. the gravitational force at the point B (2, 0, 0) is zero. c. the gravitational potential is the same at all points of the circley2 + z2 = 36.d. the gravitational potential is the same at all points on the circle y2 + z2 = 4
8. Problem 06 An ideal gas is taken from the state A (pressure /?, volume V) to the state B (pressure p/2, volume 2V) along a straight line path in the p-V diagram. Select the correct statement(s) from the following: The work done by the gas in the process A to B exceeds the work that would be done by it If the system were taken from A to B along an isotherm In the T-V diagram, the path AB becomes a part of a parabola In the p-T diagram, the path AB becomes a part of a hyperbola In going from A to B, the temperature T of the gas first increases to a maximum value and then decreases
9. Problem 07 A current I flows along the length of an infinitely long, straight, thin-walled pipe. Then the magnetic field at all points inside the pipe is the same, but not zero the magnetic field at any point inside the pipe is zero the magnetic field is zero only on the axis of the pipe the magnetic field is different at different points inside the pipe.
10. Problem 08 Two thin convex lenses of focal lengths /j and /2 are separated by a horizontal distances d (where d </f1, d < f2), and their centres are displaced by a vertical separation as shown in Fig. 1993.4. Taking the origin of coordinates, O, at the centre of the first lens, the x and y coordinates of the focal point .of this lens system, for parallel beam of rays coming from the left, are given by a. b. c. d. y = 0
11. Problem 09 A star initially has 1040 deuterons. It produces energy via the processes If the average power radiated by the star is 1016 W, the deuteron supply of the star is exhausted in a time of the order of 106 s 108 s 1012 s 1016 s
12. Problem 10 Read the following statements carefully: Y: The resistivity of semiconductor decreases with an increase in temperature. Z: In a conducting solid, the rate of collisions between free electrons and ions increases with an increase in temperature. Select the correct statement(s) from the following: Y is true but Z is false Y is false but Z is true Both Y and Z are true Y is true and Zis the correct reason for Y.
13. SECTION – II Fill in the blanks Fill in the blanks in the following. In your answer book, write down the sub-question number (I , ii, etc.), and against it write your answer corresponding to each blank. Your answer should be in the sequence (i) , (ii), etc. as given in the question paper.
14. 01 Problem A uniform rod of length L and density p is being pulled along a smooth floor with a horizontal acceleration a (see Fig. 1993.5). The magnitude of the stress at the transverse cross-section through the mid-point of the rod is ____________
15. Problem 02 A stone of mass w, tied to the end of a string, is whirled around in a horizontal circle. (Neglect the force due to gravity.) The length of the string is reduced gradually keeping the angular momentum of the stone about the centre of the circle constant. Then, the tension in the string is given by T = Arn here A is a constant, r is the instantaneous radius of the circle, and n = _________.
16. Problem 03 A container of volume 1 m3 is equally divided by a partition. One part contains an ideal gas at 300 K and the other part is vacuum. The whole system is thermally isolated from the surroundings. When the partition is removed the gas expands to occupy the whole volume. Its temperature will now be _______.
17. Problem 04 In a straight conducting wire a constant current is flowing from left to right due to a source of emu. When the source is switched off, the direction of the induced current in the wire will be _________.
18. Problem 05 In a ______ biased p-n junction, the net flow of holes is from the n region to the p region.
