3.COMBINED TEST-2 PAPER-1

COMBINED TEST 2 PAPER-1 INSTRUCTIONS PART - 1 SECTION - I (Single Correct Answer Type) This section contains 10 multiple choice questions, Each question has four choices, (A), (B), (C) and (D) out of which ONLY ONE is correct. 2. In the above question, the ratio of moment of inertia of the loop about x-axis to that about y-axis is. (A) > 1 (B) < 1 (C) = 1 (D) = 1/2 3. A particle moves along x-axis with initial position x = 0. Its velocity varies with x-coordinate as shown in graph. The acceleration 'a' of this particle varies with x as (A) (B) (C) (D) 4. A liquid soap film in shape of a plane loop has an initial area 0.05 m2. If its area is slowly doubled then the increase in its surface potential energy from its initial value will be (Surface tension of liquid = 0.2 N/m). (A) 5 × 10–2 J (B) 2 × 10–2 J (C) 3 × 10–2 J (D) None of these 5. During a rainy day, rain is falling vertically with a velocity 2m/s. A boy at rest starts his motion with a constant acceleration of 2m/s2 along a straight road. Find the rate at which the angle of the axis of umbrella with vertical should be changed so that the rain always falls parallel to the axis of the umbrella - 1 (A) 1 t2 2 (B) 1 t2 1 (C) 2  t2 (D) (D) 1 1 2t2 6. In the figure (i) an extensible string is fixed at one end and the other end is pulled by a tension T. In figure (ii) another identical string is pulled by tension 'T' at both the ends. The ratio of elongation in equilibrium of string in (i) to the elongation of string in (ii) is - (A) 1 : 1 (B) 1 : 2 (C) 2 : 1 (D) 0 7. A student is standing infront of a very high smooth vertical wall at a perpendicular separation 10m. He throws a ball towards wall and to catch the same ball he run with constant speed 2 m/s opposite to wall just after throw it. If he catches the ball after running 10 m distance. Then projection angle is (assume collision of ball with wall is elastic) : (use g = 10 m/s2)  25   30  (A)  = tan–1  6  (B)  = tan–1  8       15  (C)  = tan–1  6  (D) data is insufficient   8. Two light vertical springs with spring constants k1 & k2 and same natural lengths are separated by a distance 𝑙. Their upper ends are fixed to the ceiling and their lower ends to the ends A and B of a light horizontal rod AB. A vertical downward force F is applied at point C on the rod. AB will remain horizontal in equilibrium if the distance AC is : (A) 𝑙 2 (B) k1 k2  k1 𝑙 k2 (C) k1 (D) k2 k1  k2 9. Two persons A and B each carrying a source of frequency 596 Hz A B and 600 Hz respectively are standing at rest a few metres apart. A starts moving towards B with a velocity of 2 m/s. If the speed of sound is 300 m/s. Which of the following statement is true. (A) Beats heard per second by A is zero and B is 8. (B) Beats heard per second by A is 8 and B is zero. (C) Frequency of B heard by A is 600 Hz. (D) Frequency of A as heard by B is 604 Hz. 10. A particle of mass m moves with velocity v0 = 20 m/sec towards a wall that is moving with velocity v = 5 m/sec. If the particle collides elastically with the wall, the speed of the particle just after the collision is : (A) 30 m/s (B) 20 m/s (C) 25 m/s (D) 22 m/s SECTION – II (Multiple Correct Answers Type) This section contains 5 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE may be correct. 11. Two blocks, of masses M and 2M, are connected to a light spring of spring constant K that has one end fixed, as shown in figure. The horizontal surface and the pulley are frictionless. The blocks are released from rest when the spring is non deformed. The string is light. (A) Maximum extension in the spring is 4Mg . K (B) Maximum kinetic energy of the system is 2M2g2 K (C) Maximum energy stored in the spring is four times that of maximum kinetic energy of the system. 4M2g2 (D) When kinetic energy of the system is maximum, energy stored in the spring is K 12. A solid cube of mass 5 kg is placed on a rough horizontal surface, in xy-plane as shown. The friction coefficient between the surface and the cube is 0.4. An → external force F  6ˆi  8ˆj  20kˆ N is applied on the cube. (use g = 10 m/s2). Positive z- direction is taken vertically upwards as shown. Then pick up the correct statement(s). (A) The block starts slipping over the surface (B) The friction force on the cube by the surface is 10 N. (C) The friction force on the cube acts along the vector  3ˆi  4ˆj (D) The contact force exerted by the surface on the cube is 10 N. 13. A particle is attached to an end of a rigid rod and the other end of the rod is hinged. The rod rotates and always remains horizontal. It’s angular speed is inc→reasing at constant rate. The mass of the particle is 'm'. The force exerted by the rod on the particle is F , then : (A) F  mg (B) F is constant → (C) The angle between F and horizontal plane decreases. → (D) The angle between F and the rod decreases. 14. Hydrogen gas and oxygen gas have volume 1cm3 each at N.T.P. Then pick up the correct alternative or alternatives. (A) Number of molecules is same in both the gases. (B) The rms velocity of molecules of both the gases is the same. (C) The internal energy of each gas is the same. (D) The average velocity of molecules of each gas is the same. 15. A particle is projected from horizontal surface at speed ‘u’ at an angle (0 <  < 90º) with the horizontal such the particle lands back on same horizontal with time of flight being T0 . This time T0 is divided into four equal parts T1,T2,T3 & T4 such that for T1 and T4, acceleration acting downwards (vertically) on particle is 'a' whereas for T2 and T3 acceleration downwards is 2a. (T1,T2,T3 & T4 are time intervals in sequence from starting till end of motion). (Assume that horizontal acceleration of particle is always zero) (A) At the ends of time T1 and T3 , height of particle from horizontal will be same (B) Final velocity of particle just before landing will be equal to initial velocity of projection of particle. (C) Vertical component of velocity of particle will be same at the end of T1 and T3 (D) Horizontal component of velocity of particle at the end of T2 and T3 will be same SECTION - III (Integer Answer Type) This section contains 5 questions. Answer each of the questions in a single-digit integer, ranging from 0 to 9. 16. Liquid is coming out of the small hole P at the bottom of large vessel containing three different liquids of densities , 2 and 3 with their height levels maintained 3h, 2h and h respectively as shown in the figure. Find the velocity of the liquid if  = 100 kg/m3 and h = 0.24 m. (g = 10 m/s2) 17. A solid uniform sphere of radius r rolls without sliding along the inner surface of a fixed spherical shell of radius R and perform small oscillations. Find the angular frequency of these oscillation. Take g =9.8 m/s2 , R = 10 m, r = 3m. 18. Ice at 0ºC is added to 200 gm of water initially at 70ºC in a vaccum flask. When 50 gm of ice has been added and has all melted the temperature of the flask and its contents is 40ºC. When a further 80 gm of ice has been added and has all melted, the temperature of the whole becomes 10ºC. The latent heat of fusion of ice is L cal/ L gm find 10 . 19. A satellite goes along a circular path of radius 2 × 108 m around the earth of mass 1024 kg. Find the value of 'a' if the rate of change of area swept by the line joining earth and the satellite is (a×7×109)m2/s. 20. A man standing in front of a mountain beats a drum at regular intervals. The druming rate is gradually increased and he finds that the echo is not heard distinctly when the rate becomes 40 per minute.He then moves towards mountain by 90 m and finds that echo is again not heard when drumming rate becomes 60 per minute. Find the ratio of distance between the mountain and the initial position of the man and the distance by which he moved. ANSWER KEY TO COMBINED TEST - 02 (PAPER - 1) 1. (B) 2. (B) 3. (A) 4. (B) 5. (A) 6. (A) 7. (A) 8. (D) 9. (B) 10. (A) 11. (A,B,C) 12. (B,C,D) 13. (C,D) 14. (A,C,D) 15. (A,D) 16. 4 17. 1 18. 9 19. 8 20. 3 PART-2