Title 19TH MAY PAPER.pdf ✅

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PHYSICS 1. Two masses 4m and 9m move with equal KE. The ratio of the magnitude of their momenta is (A) 1 : 2 (B) 2 : 3 (C) 1 : 3 (D) 3 : 1 2. The centre of mass of a body (A) lies always outside the body (B) may lie within, outside or on the surface of body (C) lies always inside the body (D) lies always on the surface of the body 3. If no external force acts on a system (A) velocity of centre of mass remains constant (B) position of centre of mass remains constant (C) acceleration of centre of mass remains non- zero and constant (D) All of the above 4. A uniform force of ˆ ˆ (5i 5j)N  acts on particle mass 1 kg. The particle moves from 1 ˆ ˆ r (3i 4j)   to 2 ˆ ˆ r (5i 8j)   under this force. The work done by the force is (A) 20 J (B) 25 J (C) 30 J (D) 50 J 5. Two bodies of masses m1 and m2 have equal kinetic energies. If 1 p and 2 p are their respective momentum, then ratio 1 2 p : p is equal to (A) m : m 1 2 (B) m : m 2 1 (C) m : m 1 2 (D) 2 2 m : m 1 2 6. If a force of 9 N is acting on a body, then find instantaneous power supplied to the body when its velocity is 5 m/s in the direction of force (A) 195 watt (B) 45 watt (C) 75 watt (D) 100 watt 7. The bob of simple pendulum having length l, is displaced from mean position to an angular position  with respect to vertical. If it is released, then velocity of bob at equilibrium position will be (A) 2g (1 cos ) l   (B) 2g (1 cos ) l   (C) 2g cos l  (D) 2gl 8. In an inelastic collision (A) momentum of the system is always conserved (B) velocity of separation is less than the velocity of approach (C) the coefficient of restitution can be zero (D) All of the above 9. Initially mass m is held such that spring is in relaxed condition. If mass m is suddenly released, maximum elongation in spring will be (A) mg k (B) 2mg k (C) mg 2k (D) mg 4k 10. Moment of inertia of a hollow cylinder of mass M and radius r about its own axis is (A) 2 2 Mr 3 (B) 2 2 Mr 5 (C) 1 2 Mr 2 (D) Mr2 11. The kinetic energy acquired by a body of mass m is travelling some distance s, starting from rest under the actions of a constant force, is directly proportional to (A) m0 (B) m (C) m2 (D) m 12. Two particles A and B initially at rest move towards each other under a mutual force of attraction. At the instant when velocity of A is v and that of B is 2v, the velocity of centre of mass of the system (A) v (B) 2v (C) zero (D) cannot be determine 13. Ratio of maximum to minimum tension in vertical circular motion is 3, then find maximum tension in vertical circular path if mass of object is ‘m’. (A) 4 mg (B) 4mg 3 (C) 3mg 4 (D) 9 mg PW-AITS_NT-02
14. A uniform chain is held on a frictionless table with one-fifth of its length hanging over the edge. If the chain has a length l and a mass m, how much work is required to pull the hanging part back on the table? (A) mgl /10 (B) mgl /5 (C) mgl /50 (D) mgl /2 15. A pump is required to lift 800 kg of water per minute from a 10 m deep well and eject it with speed of 20 m/s. The required power in watts of the pump will be (assume g = 10 m/s2 ) (A) 6000 (B) 4000 (C) 5000 (D) 8000 16. A body is projected at an angle  with the horizontal. When it is at highest point, then the ratio of the potential and kinetic energies of the body is (A) tan  (B) tan2 (C) 2u gsin  (D) u gsin  17. A block of mass of 1 kg slides down a curved track that is one quadrant of circle of radius 1 m. Its speed at the bottom in 2 m/s. the work done by the frictional force is: (g = 10 m/s2 ) (A) 8 J (B) –8 J (C) 4 J (D) –4 J 18. Which of the following is invalid equation? (where , , L and  have their usual meanings) (A)   I (B) L I   (C)   I (D) All of these 19. A ball of mass 5 kg moving with speed 8 m/s collides head on with another stationary ball of mass 15 kg. If collision is perfectly inelastic, then loss in kinetic energy is (A) 160 J (B) 80 J (C) 40 J (D) 120 J 20. Two blocks, each of mass m moving with speed v, collide with the spring of force constant k as shown in figure. The maximum compression of the spring is: (A) 2 mv k (B) 2 2mv k (C) 2 mv 2k (D) zero 21. A 50.0-kg boy runs at a speed of 10.0 m/s and jumps onto a cart as shown in the figure. The cart is initially at rest. If the speed of the cart with the boy on it is 2.50 m/s, what is the mass of the cart? (A) 150 kg (B) 175 kg (C) 210 kg (D) 260 kg 22. The potential energy of a certain spring when stretched through a distance ‘S’ is 10 joule. The amount of work (in joule) that must be done on this spring to stretch it through an additional distance ‘S’ will be (A) 30 (B) 40 (C) 10 (D) 20 23. A particle is acted by a conservative force F = kx, where k is a +ve constant. Its potential energy at x = 0 is zero. Which curve correctly represents the variation of potential energy of the block with respect to x (A) (B) (C) (D) 24. The separation between carbon and oxygen atoms in CO is 1.2 Å. The distance of centre of mass from carbon atom is (A) 0.21 Å (B) 0.69Å (C) 0.91 Å (D) 0.43Å 25. Two bodies of mass 1 kg and 3 kg have position vectors ˆ ˆ ˆ i 2j k   and ˆ ˆ ˆ    3i 2j k respectively. The center of mass of the system has a position vector. (A) ˆ ˆ   2i 2k (B) ˆ ˆ ˆ    2i j k (C) ˆ ˆ ˆ 2i j k   (D) ˆ ˆ ˆ    i j k 26. A bullet weighing 50 gm leaves the gun with a velocity of 30 ms–1 . If the recoil speed imparted to the gun is 1 ms–1 , the mass of the gun (A) 1.5 kg (D) 15 kg (C) 20 kg (D) 30 kg 27. A jet of water hits a flat stationary plate perpendicular to its motion. The jet ejects 500g of water per second with a speed of 1 m/s. Assuming that after striking, the water flows parallel to the plate, then the force exerted on the plate is (A) 5 N (B) 1.0 N (C) 0.5 N (D) 10 N
28. A ring and a disc of the same radius have the same moment of inertia about an axis of rotation passing through its centers and perpendicular to their planes. The mass of the ring and disc are in the ratio (A) 1 2 (B) 2 (C) 1 2 (D) 2 29. The angular momentum of a system of particle is conserved (A) when no external force acts upon the system (B) when no external torque acts upon the system (C) when no external impulse acts upon the system (D) when axis of rotation remains same 30. For equilibrium of the system, value of mass m shoule be (A) 9 kg (B) 15 kg (C) 21 kg (D) 1 kg 31. Two equal and opposite forces are applied tangentially to a uniform disc of mass M and radius R as shown in the figure. If the disc is pivoted at its centre and free to rotate in its plane, the angular acceleration of the disc is (A) F MR (B) 2F 3MR (C) 4F MR (D) zero 32. A disc is rolling (without slipping) on a horizontal surface. C is the centre, P and Q are two points equidistant from C. Let vP, vQ and vC be the magnitudes of velocities of points P, Q and C respectively, then: (A) vQ > vC > vP (B) vQ < vC < vP (C) Q P C p 1 v v , v v 2   (D) vQ < vC > vP 33. A solid cylinder of mass M and radius R rolls without slipping down an inclined plane of length L and height h. What is the speed of its centre of mass when the cylinder reaches its bottom: (A) 2gh (B) 3 gh 4 (C) 4 gh 3 (D) 4gh 34. When a sphere rolls down an inclined plane, then identify the correct statement related to the work done by friction force rolling without slipping (A) The friction force does positive translational work (B) The friction force does negative rotational work (C) The net work done by friction is zero (D) All of the above 35. A circular table rotates about a vertical axis with a constant angular speed . A circular pan rests on the turn table (with the centre coinciding with centre of table) and rotates with the table. The bottom of the pan is covered with a uniform small thick layer of ice placed at centre of pan. The ice starts melting. The angular speed of the turn table (A) remains the same (B) decreases (C) increases (D) may increase or decrease on the thickness of layer 36. A circular hoop rolls without slipping on a flat horizontal surface. Which one of the following necessarily true? (A) All points on the rim of the hoop have the same speed. (B) All points on the rim of the hoop have the same velocity. (C) Every point on the rim of the wheel has different velocity. (D) All points on the rim of the hoop have acceleration vectors that are tangent to the hoop. 37. The ratio of the total K.E. of a rolling disc to its rotational K.E. is (A) 1 : 3 (B) 1 : 2 (C) 2 : 1 (D) 3 : 1 38. Moment of inertia of a disc of mass M and radius r about its tangent and perpendicular to the plane, is (A) 1 2 Mr 2 (B) 2Mr2 (C) Mr2 (D) 3 2 Mr 2 39. A bomb of 12 kg explodes into two pieces of masses 4 kg and 8 kg. The velocity of 8 kg mass is 6 m/sec. The kinetic energy of the other mass is (A) 48 J (B) 32 J (C) 24 J (D) 288 J 40. Potential energy of a particle at position x is given by U = x 2 – 5x. Which of the following is equilibrium position of the particle? (A) x = 0 (B) x = 5 (C) x = 2.5 (D) x = 7.5