11.Combined Test-2 (Paper-1)

RRR_CT-2_XII PAPER - 1 PART - I : PHYSICS SECTION – I (Single Correct Answer Type) This section contains 8 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct. 1. Find maximum amplitude for safe SHM(block does not topple dur- ing SHM) of a uniform cubical block of side 'a' on a smooth hori- zontal floor as shown in figure (sptring is massless) : (A) mg (B) 3mg 2K (C) 3mg 4K K (D) 3mg 2K 2. In the figure shown, the pulleys and strings are massless. The acceleration of the block of mass 4m just after the system is released from rest is 3 ( = sin–1 5 ) 2g (A) 5 2g downward (B) 5 upwards (C) 5 g 11 upwards (D) 5 g downwards 11 3.. In the figure shown, a light container is kept on a horizontal rough surface of coefficient of friction  = Sh . A very small hole of area S is made at depth 'h'. V Water of volume 'V' is filled in the container. The friction is not sufficient to keep the container at rest. The acceleration of the container initially is V (A) Sh g (B) g (C) zero (D) Sh g V 4. A solid sphere of iron at 2°C is lying at the bottom of a bucket full of water at 2°C. If the temperature of the water is increased to 3°C, the buoyant force on the sphere due to water will. (A) Increase (B) Be unchanged (C) Decrease (D) Increase or decrease depends upon the numerical values of coefficient of expansion of water and iron. 5. Two sources S1 and S2 of same frequency f emits sound. The sources are moving as shown with speed u each. A stationary observer hears that sound. The beat frequency is (v = velocity of sound) (A) (C) 2u2f v2  u2 2uv f v2  u2 (B) (D) (D) 2 v2 f v2  u2 2u f v 6. A body performs SHM along the straight line segment ABCDE with C as the mid point of segment AE (A and E are the extreme position for the SHM). Its kinetic energies at B and D are each one fourth of its maximum value. If length of segment AE is 2R, then the distance between B and D is (A) 3 2 R (B) 7. A wall is made of two layers A and B of the same thickness but different materials as shown. The thermal conductivity of A is thrice that of B. In steady state, the temperature difference across the wall is 360C. The temperature difference across the layer A is : (A) 60 C (B) 90 C (C) 180 C (D) 270 C 8. Man A is sitting in a car moving with a speed of 54 km/hr observes a man B in front of the car crossing perpendicularly a road of width 15 m in three seconds. Then the velocity of man B (in m/s) will be: (A) 5 towards thecar at some angle (5 dqN dks.k ij dkj dh rjQ) (B) 5 10 away from thecar at someangle(5 dqN dks.k ij dkj ls nwj dh rjQ) (C) 5 perpendicular to theroad (5 lM+d ds yEcor~) (D) 15alongtheroad(15 lM+d ds vuqfn'k) 9. In the figure shown, the minimum force F to be applied perpendicular to the incline so that the block does not slide is : (The block is always in contact with the incline) (A) 0 (B) 40 N (C) 120 N (D) 200 N 10. A large open tank has two small holes in its vertical wall as shown in figure. One is a square hole of side 'L' at a depth '4y' from the top and the other is a circular hole of radius 'R' at a depth ‘y’ from the top. When the tank is completely filled with water, the quantities of water flowing out per second from both holes are the same. Then, 'R' is equal to : (A) (B) 2L (C) MCQ L . L (D) 2 11. A steel wire is rigidly fixed at both ends. Its length, mass and cross sectional area are 1m, 0.1kg and 10-6 m2 respectively. Then the temperature of the wire is lowered by 20 oC. If the transverse waves are setup by plucking the wire at 0.25m from one end and assuming that wire vibrates with minimum number of loops possible for such a case. (A) The tension in the wire will be 48.4 N. (B) The number of loops will be 2. (C) The frequency of vibration will be 22 Hz. (D) The frequency of vibration will be 44 Hz. 12. In the figure shown, coefficient of restitution between A and B is e = 1 , then : 2 (A) velocity of B after collision is v (B) impulse between two during collision is 3 mv 2 4 3 1 (C) loss of K.E. during collision is 16 mv2 (D) loss of K.E. during collision is 4 mv2 13. An experiment measures quantities a, b, c and x is calculated from x = b, c are ± 1%, ± 3% and ± 2% respectively. ab2 c3 . If the percentage errors in a, (A) The percentage error in x can be ± 13% (B) The percentage error in x can be ± 7% (C) The percentage error in x can be ± 20% (D) The percentage error in x can be ± 26% 14. A metal wire of length L, area of cross-section A and Young’s modulus Y is stretched by a variable force F such that F is always slightly greater than the elastic force of resistance in the wire. When the elongation of the wire is 𝑙 : (A) the work done by F is (B) the work done by F is YA2 L YA𝑙2 2L YA𝑙2 (C) the elastic potential energy stored in the wire is 2L (D) heat is produced during the elongation 15. A balloon moves up with a velocity 5 m/s .A stone is thrown from it with a horizontal velocity 2 m/s relative to it. The stone hits the ground at a point 10 m horizontally away from it. (Take g = 10 m/s2) (A) the time of flight of the stone is 5 s (B) height of the balloon at the time of throwing the stone is 100 m. (C) the speed with which it will hit the ground is 40 m/s (D) the time of flight of the stone will increase if the horizontal velocity of the stone is increased. Integer Answer Type 16. A small block is kept on a platform executing SHM along the x-axis described by x = A sint. The time period of SHM is T and the coefficient of friction between the block and the platform is . The condition that the block   x2A does not slip on the platform at any instant is gT2 , find the value of ‘x’. 17. A solid cube of side a, density d and specific heat 's' is at temperature 400 K. It is placed in an ambient temperature of 200 K. Take : a = 0.9 m, d = 4.8 × 103 Kg/m3, s = 2.0 × 103 J/kg-K, Stefan's constant  = 6 × 10–8 W/K4-m2. Consider the cube to be a black body. If the time for the temperature of the cube to drop by 5 K is 1000 X seconds, find X in nearest integer. 18. A solid spherical planet has a very narrow tunnel along the diameter. Mass of the planet is 5 × 1024 kg, radius 20 of the planet is 4 × 105 m and value of G is 3 × 10–11 N.m2/kg2. If a particle is at its centre, its escape speed is (x) × 104 m/sec. Find the value of x. 19. A uniform board of length L and weight W is balanced on a fixed semicircular cylinder of radius R as shown in the figure. The plank is tilted slightly from its equilibrium position, if the period of its oscillations is then find x ? [g = 2] 20. The co-efficient of thermal expansion of a rod is temperature dependent and is given by the formula  = a T, where a = 1 𝑙n2 °C–2 and T in ºC. If the length of the rod is 𝑙 at temperature 0 ºC, then find the 2 temperature (in °C) at which the length will be 2𝑙. ANSWERKEY 1. (D) 2. (D) 3. (D) 4. 5. (C) 6. (C) 7. (B) 8. (B) 9. (D) z 10. (C) MCQ 11. (A), (B), (C) 12. (B) , (C) 13. (AB) 14. (B), (C) 15. (A) , (B) Integer Answer Type 16. x = 4 17. 05 18. 5 19. 3 20. 2