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Position of Center of Mass, , Position of center of mass, , (d) The CM is on the line joining them at a point, whose distance from each particle is proportional, to the mass of that particle., 2. The center of mass a system of particles does not, depend on:, (a) Masses of the particles, (b) Forces on the particles, (c) Position of the particles, (d) Relative distance between the particles, 3. The Centre of mass of a system of two particles, divides the distance between them, (a) In inverse ratio of square of masses of particles, (b) In direct ratio of square of masses of particles, (c) In inverse ratio of masses of particles, (d) In direct ratio of masses of particles, 4. A system consists of mass M and m(<<M). the, canter of mass of the system is:, (a) At the middle, (b) nearer to M, , (c) nearer to m (d) at the position of larger, mass., 5. In a carbon monoxide molecule, the carbon and the, oxygen atoms are separated by a distance 1.12 x 1010, m. the distance of the Centre of mass from the, carbon atoms is:, (a) 0.48 1010 m, (b) 0.511010 m, , (c) 0.56 1010 m, , (d) 0.64 1010 m, , 6. Two bodies of mass 1 kg and 3 kg have position, 1. Choose the correct statement about the center of, mass (CM) of a system of 2 particles:, (a) The CM lies on the line joining two particles, midway between them, (b) The CM lies on the line joining them at a point, whose distance from each particle is inversely, proportional to the mass of that particle., (c) The CM lies on the line joining them at a point, whose distance from each particle is proportional, to the square of the mass of that particle, , ^, , ^ ^, , ^, , ^, , ^, , vectors i  2 j k and 3 i  2 j  k respectively. The, centre of mass of this system has position vector:, ^, , ^, , ^, , ^, , ^, , (a)  i  j  k, ^, , (c) 2i  j  k, , ^, , ^, , (b) 2 i  2 k, ^, , ^, , ^, , (d) 2 i  j k, , 7. Three masses are placed on the x-axis: 300 g at, origin, 500 g at x =40 cm and 400 g at x = 70 cm., The distance of the centre of mass form the origin is:, (a) 50 cm, (b) 30 cm, , (c) 40 cm, , (d) 45 cm.

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8. The center of mass of a body:, (a) Lies always outside the body, (b) May lie within, outside or on the surface of, the body., (c) Lies always inside the body, (d) Lies always on the surface of the body, , Single choice questions (Level 1), 9. A uniform metal disc of radius R is taken and out of, it a disc of diameter R is cut off from the end. The, center of mass of the remaining part will be:, , R, from the center, 4, R, (b), from the center, 5, (a), ,  2a 2b , , ,  3 3 ,  3a 3b , (c)  , ,  4 4, (a) , ,  5a 5b , , ,  3 3, , (b) , , (d), , 15. Three particles of masses 50g, 100g and 150g are, placed at the vertices of an equilateral triangle of, side 1 m (as shown in the figure). The (x, y), coordinates of the center of mass will be, , R, from the center, 6, R, from the center, 3, , 10. A circular plate of diameter, d is kept in contact with a, square plate of edge d as, shown in the figure. The, a, a, density of the material and, the thickness are same everywhere. The centre of, mass of the composition system will be, (a) inside the circular plate, (c) at the point of contact, (b) inside the square plate, (d) outside the system, 11. The centre of mass of a system of particles is at the, origin. It follows that, (a) the number of particles to the right of the origin, is equal to the number of particles to the left, (b) the total mass of the particles to the right of the, origin is same that as the total mass to the left of, the origin, (c) the number of particles on X-axis should be, equal to number of particles on Y-axis, (d) If there is a particle on +ve X- axis, there must, be at least one particle on –ve X-axis, (e) None of the above, 12. All the particles of a body are situated at a distance, R, from the origin. The distance of the centre of mass of, body from the origin is, (a)  R, (b)  R, (c) > R, (d)  R, 13. Four particles of mass m1 = 2 m, m2 = 4 m, m3 = m, and m4 are placed at four corner’s of a square. What, should be the value of m4 so that the centre of mass, of all the four particles are exactly at the centre of, the square?, (a) 2 m, (b) 8 m (c) 6 m, (d) none of these, 14. A uniform rectangular thin sheet ABCD of mass M, has length a and breadth b, as shown in the figure. If, the shaded portion HBGO is cut-off, the coordinates, of the center of mass of the remaining portion will, be:-, ,  3, 3 , m,, m , 12, 8, , , ,  3, 5 , m, m , 12 ,  4, , (a) , , , (b) , , , (c), ,  3, 7 , m, m , (d) , 12 ,  8, , 16. Two identical thin uniform rods each of mass m and, length Lare joined as shown in the figure. The x and, y coordinates of center of mass system form O is, , (a), , L 3L, L 3L, L 3L, L 3L, ,, (b)  ,, (c) ,, (d) ,, 4 8, 8 4, 4 2, 2 4, , 17. Three masses of 2 kg, 4 kg and 6 kg are placed at the, three points (2, 0, 0), (3, 2, 0) and (0, 2, 0), respectively. The position vector of their center of, mass is, , 5^ 4 ^, i j, 3 3, 2^ 7 ^, (c) i  j, 3 3, (a), , 4^ 5 ^, i j, 3 3, 7^ 2 ^, (d) i  j, 3 3, (b), , 18. From a circular disc of radius 4R, two small circular, discs each of radius Rare cut off as shown. The, center of mass of the remaining disc will be, , R^ R ^, i j, 5, 5, 3R ^ ^, (i  j ), (c), 14, (a), , MEDJEE CLASSES 4/641 Vijyant Khand Gomtinagar Lucknow, contact 991922289, , (b), , R ^ R ^, i j, 5, 5, , (d) None of these

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19. Four particles A, B, C and D with masses mA = m,, mB = 2 m, mC = 3 and mD = 4 m are at the corners of, a square. They have accelerations of equal, magnitude with directions as shown. The, acceleration of the center of mass of the particles is:, , (a), , a ^ ^, (i  j ), 5, , (b), , a ^ ^, (i  j ), 5, ^, , (c) Zero, , ^, , (d) a (i  j ), , Velocity & acceleration of Center of Mass, , Single choice questions (Level 0 & 1), 20. A 2 kg body and a 3 kg body are moving along the, x-axis At a particular instant the 2 kg body has a, velocity of 3 ms-1 and 3kg body has the velocity of, 2 ms-1. The velocity of the centre of mass at that, instant is:, (a) 5 ms-1, (b) 1 ms-1, (c) 0, (d) none of these, 21. Two object of masses 200 gm and 500 gm posses, ^, , ^, , ^, , velocities 10 i m/s and 3 i  5 j m/s respectively., The velocity of their center of mass in m/s is:, ^, , ^, , (a) 5 i  25 j, ^, , (c) 5 i , , 25 ^, j, 7, , ^, 5^, i  25 j, 7, ^ 5 ^, (d) 25 i  j, 7, , (b), , slightly and released,, When the rod finally, falls on the horizontal, x axis, surface the lower end, x=0, will remain at, (a) x = l/2 (b) x > l/2, (c) x < l/2 (d) x = 0, 24. Consider a system of two identical particles. One, of the particles is at rest and the other has an, acceleration a. The centre of mass has an, acceleration, , , , (a) zero, (b) 1/2 a, (c) a, (d) 2 a, 25. If the system is released, then the acceleration the, center of mass of the system:, , 22. Two blocks of masses 10 kg and 4 kg are, connected by a spring of negligible mass and, placed on a frictionless horizontal surface. An, impulse gives a velocity of 14 m/s to the heavier, g, g, (a), (b), block in the direction of the lighter block. The, 4, 2, velocity of the centre of mass is, (c) g, (d) 2g, (a) 30m/s, (b) 20m/s (c) 10m/s, (d) 5m/s, 7. For the system shown in figure the acceleration of, 23. A uniform rod of length l is kept vertically on a, center of mass is, rough horizontal surface at x = 0. It is rotated, MEDJEE CLASSES 4/641 Vijyant Khand Gomtinagar Lucknow, contact 991922289

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(b) 2.4iˆ  3.6 ˆj m/s2, (c) 3.6iˆ  2.4 ˆj m/s2, (d) 3.6iˆ  2.4 ˆj m/s2, , (a) 2.4iˆ  3.6 ˆj m/s2, , Conservation of linear momentum, , Single choice questions (Level 0), 26. Two bodies of masses 2 kg and 4 kg are moving, with velocities 20 m/s and 10m/s towards each, other due to mutual gravitational attraction. What, is the velocity of their Centre of mass?, (a) 5.3 ms-1, (b) 6.4 ms-1, , (c) zero, , (d) 8.1 ms-1, , 27. Two spheres of masses 2M and M are initially at, rest at a distance R apart. Due to mutual force of, attraction, they approach each other. When they, are at separation R/2, the acceleration of the, center of mass of spheres would be:, , (a) 0 m/s2, (c) 3g m/s2, , (b) g m/s2, (d) 12g m/s2, , 28. A cart of mass M is tied to one end of a massless, rope of length 10 m. the other end of the rope is, in the hands of a man of mass M, the entire, system is on a smooth horizontal surface. The, man is at x = 0 and the cart at x = 10 m. if the, man pulls the cart by a rope the man and the cart, will meet at the point:, (a) X = 0, (b) x = 5 m, (b) X = 10 m (d) They will never meet., 29. Two persons of masses 55 kg and 65 kg, respectively, are at the opposite end of a boat., The length of the boat is 3.0 m and weight 100, kg. the 55 kg man walks upto the 65 kg man and, sits will hm. If the boat is in still water, the center, of mass of the system shifts by:, , (a) zero, (c) 3.0 m, , 30. Consider a two particle system with particles, having masses m1 and m2. If the first particle is, pushed towards the center of mass through s, distance d, by what distance should the second, particle be moved so as to keep the center of mass, at the same position?, , (b) 0.75 m, (d) 2.3 m., , m1, d, m2, m, (c) 2 d, m1, (a), , (b) d, (d), , m1, d., m1  m2, , 31. Two bodies of masses 0.1 kg and 0.4 kg move, towards each other with the velocities 1m/s and, 0.1 m/s respectively. After collision they stick, together. In 10 sec the combined mass travels, (a) 120m, (b) 0.12 m, (c) 12 m, (d) 1.2m, 32. An object of mass 2 kg is moving with a velocity, of 3 ms-1 and collides head on with an object of, mass 1 kg moving in the opposite direction with a, velocity of 4 ms-1. After collision both the object, so that they move with a common velocity equal, to:, (a), , 2 1, ms, 3, , (b) 1 ms-1, , (c) 2 ms-1, (d) 3 ms-1, 33. A shell is fired from a canon with velocity v at an, angle  with the horizontal direction. At the, highest point in its path it explodes into two, pieces of equal masses. One of the pieces retraces, , MEDJEE CLASSES 4/641 Vijyant Khand Gomtinagar Lucknow, contact 991922289

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its path to the cannon. The speed of the other, piece immediately after the explosion is:, (a) (, , 3, ) vcos , 2, , (c) 2v cos , , (b), , 3, 2, , (d) ( ) v cos , , 34. A bomb of mass 3.0 kg explodes in air into two, pieces of masses 2.0 kg and 1.0 kg. The smaller, mass goes a speed of 80 m/s. The total energy, imparted to the two fragments is:, (a) 0.07kJ, (b) 2.14 kJ, (c) 2.4 kJ, (d) 4.8 kJ, 35. A nucleus of mass number A, originally at rest,, emits an  -particle with speed v. The daughter, nucleus recoils with a speed., (a), (c), , 2v, A 4, , 4v, A 4, 2v, (d), A4, (b), , 36. A stationary particle explodes into two pieces of, masses m1 and m2 which move in opposite, directions with velocities v1 and v2. The ratio of, their kinetic energies E1/E2 is, (a) 1, (b) m1/m2, (c) m2/m1, (d) m1v2/m2v1, 37. A bomb of mass 9 kg explodes into two pieces of, masses 3 kg and 6 kg. The velocity of mass 3 kg, is 16 m/s. The K.E. of mass 6 kg (in joule) is, (a) 96, (b) 384, (c) 192, (d) 768, 38. If the net force acting on the system of particles, is zero, then which of the following may vary, (a) Momentum of the system, (c) Velocity of centre of mass, (b) Kinetic energy of the system, (d) Position of centre of mass, 39. A bullet is fired from a rifle recoils freely,, determine whether the kinetic energy of the rifle, (a)is greater than bullet., (b)equal to the bullet., (c)Less than the bullet, (d)will not recoil, 40. A bomb of mass 16 kg at rest explodes into two, pieces of masses 4 kg and 12kg. The velocity of, the 12kg mass is 4ms-1. The kinetic energy of the, other mass is, (a) 144 J, (b) 288 J, (c) 192 J, (d) 96J, 41. A bomb of mass 1 kg is thrown vertically upwards, with a speed of 100 m/s. After 5 seconds at, explodes into two fragments. One fragment of, mass 400gm is found to go down with a speed of, 25m/s. What will happen to the second fragment, just after the explosion ? (g = 10m/s2), (a) It will go upward with speed 40 m/s, (b) It will go upward with speed 100 m/s, (c) It will go upward with speed 60 m/s, (d) It will also go downward with speed 40 m/s, 42. A shell of mass 200 gm is ejected from a gun of, mass 4 kg by an explosion that generates 1.05 kJ, of energy. The initial velocity of the shell is, , (a) 100 ms-1, (b) 80 ms-1, -1, (c) 40 ms, (d) 120 ms-1, 43. A mass m moving horizontal (along the x-axis), with velocity v collides and sticks to mass of 3m, moving vertically upward (along the y-axis) with, velocity 2v. The final velocity of the combination, 1 ˆ 3 ˆ, 1, 2, vi  vj, (b) viˆ  vjˆ, 4, 2, 3, 3, 3 ˆ 1 ˆ, 2 ˆ 1 ˆ, (c) vi  vj (d) vi  vj, 2, 4, 3, 3, , (a), , 44. A 238U nucleus decays by emitting an alpha, particle of speed v ms-1.The recoil speed of the, residual nucleus is (in ms-1), (a) -4v / 234 (b) v / 4, (c) -4v/238 (d), 4v/238, 45. A body of mass 50 kg is projected vertically, upwards with velocity of 100 m/sec. 5 seconds, after this body breaks into 20 kg and 30 kg . If 20, kg piece travels upwards with 150 m/sec, then the, velocity of other block will be, (a) 15m/sec downwards, (b) 15 m/sec upwards, (c) 51 m/sec downwards, (d) 51 m/sec upwards, , Single choice questions (Level 1), 46. Consider the following two statements., (1) Linear momentum of a system of particles is, zero., (2) Kinetic energy of system of particles is zero., (a) A does not imply B and B does not imply A., (b) A implies B but B does not imply A, (c) A does not imply B but b implies A’, (d) A implies B and B implies A., 47. A body falling vertically downwards under gravity, breaks in two parts of unequal masses. The centre, of mass of the two parts taken together shifts, horizontally towards, (a) heavier piece, (b) does not shift horizontally, (c) lighter piece, (d) depends on the vertical velocity at the time of, breaking, 48. A ball kept in a closed box moves in the box, making collisions with the walls. The box is kept, on a smooth surface. The velocity of the centre of, mass, (a) of the box remains constant, (b) of the box plus the ball system remains, constant, (c) of the ball remains constant, (d) of the ball relative to the box remains constant, 49. Internal forces can change, (a) the linear momentum but not the kinetic, energy, (b) the kinetic energy but not the linear, momentum, (c) linear momentum as well as kinetic energy, (d) neither the linear momentum not the kinetic, energy, , MEDJEE CLASSES 4/641 Vijyant Khand Gomtinagar Lucknow, contact 991922289

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50. A man of 50 kg mass is standing in a gravity free, space a height of 10 m above the floor. He throws, a stone of 0.5 kg mass downwards with a speed, 2m/s. when the stone reaches the floor, the, distance of the man above the floor will be, (a) 10m, (b) 20 m, , (c) 9.9 m, , m, before, collision, , 51. Two spherical bodies of mass M and 5 M and radii, R and 2R are released in free space with initial, separation between their centers equal to 12 R. if, they attract each other due to gravitational force, only, then the distance covered by the smaller, body before collision is:, , ^, , (b) 7.5 R, (d) 2.5 R, , ^, , ^, , mass flies off with a velocity (100 i  35 j  8 k ) ., The velocity of the larger pieces will be, ^, , ^, , ^, , ^, , ^, , (a) 4 i  23 j  16 k (b) 100 i  35 j  8 k, ^, , ^, , ^, , ^, , 2v, , (c), , ^, , ^, , ^, , ^, , (c) 20 i  15 j  80 k (d) 20 i  15 j  80 k, 53. An isolated particle of mass m is moving in, horizontal plane(x-y), alone the x-axis, at a certain, height above the ground, it suddenly explodes into, two fragments of masses m/4 and 3m/4 .An instant, later, the smaller fragment is at y = +15cm.The, larger fragment at this instant is at, (a) y = -5cm, (b) y = +20cm, (c) y = +5cm, (d) y = -20cm, 54. A small sphere of radius R held against the inner, surface of a smooth spherical shell of radius 6 R as, y, shown in the figure. The, masses of the shell and small, spheres are 4 M and M, respectively. This, arrangement is placed on a, smooth horizontal table. The, O, small sphere is now released., The x-coordinate of the centre of the shell when, the smaller sphere reaches the other extreme, position is, (a) R (b) 2 R, (c) 3 R, (d)4 R, 55. A mass ‘m’ moves with a velocity ‘v’ and collides, inelastically with another identical mass. After, collision the 1st mass moves with velocity, , v, 3, , in a, , direction perpendicular to the initial direction of, motion. Find the speed of the 2nd mass after, collision., , (c), , v, , (d), , 3, , (a) 10 2 m / s, , ( 20 i  25 j  12 k ) suddenly breaks in two pieces, whose masses are in the ratio 1 : 5. The smaller, , ^, , (b) v, , 2, 3, , v, , 56. A 1 kg stationary bomb is exploded in three parts, having mass ratio 1 : 1 : 3, parts having mass same, move in perpendicular directions with velocity, 30m/s, then the velocity of bigger part will be:, , 52. An object flying in air with velocity, ^, , 3v, , (a), , (d) 10.1 m, , (a) 4.5 R, (c) 1.5 R, , v/ 3, after, collision, , m, , x, , 10, m/s, 2, (d) v / 2, (b), , 57. An explosion breaks a rock into three parts in a, horizontal plane. Two of them go off at right, angles to each other. The first part of mass 1 kg, moves with a speed of 12 ms-1 and the second part, of mass 2 kg moves with 8 ms-1 speed. If the third, part flies off with 4 ms-1 speed, then its mass is:, [AIPMT 2013], (a) 5 kg, (b) 7kg, (c) 17 kg, (d) 3 kg, 58. A bullet of mass 10 g moving horizontally with a, velocity of 400 ms-1 strickes a wooden block of, mass 2 kg which is suspended by a light, inextensible string of length 5m. As a result, the, centre of gravity of the block is found to rise a, vertical distance of 10 cm. The speed of the bullet, after it emerges out horizontally from the block, will be, (a) 160 ms-1 (b) 100 m s-1, (c) 80 ms-1, (d) 120 m s-1, 59. A piece of wood of mass 0.03 kg is dropped from, the top of a 100 m height building. At the same, time, a bullet of mass 0.02 kg is fired vertically, upward, with a velocity 100 ms-1, from the ground., The bullet gets embedded in the wood. Then the, maximum height to which the combined system, reaches above the top of the building before falling, below is: [g = 10 ms-2], (a) 30m, (b) 10m, (c) 40m, (d) 20m, 60. A body of mass m1 moving with an unknown, ^, , velocity of v1 i , undergoes a collinear collision, with a body of mass m2 moving with a velocity, ^, , v2 i . After collision, m1 and m2 move with, ^, , ^, , velocities of v3 i and v4 i , respectively If m2 =, 0.5 m1 and v3 = 0.5 v1, then v1 is:-, , (a) v4 , , v2, 4, , (b) v4 , , MEDJEE CLASSES 4/641 Vijyant Khand Gomtinagar Lucknow, contact 991922289, , v2, 2

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(c), , (d) v4  v2, , 61. A particle of mass ‘m’ is moving with speed ‘2V’, and collides with a mass ‘2m’ moving with speed, ‘v’ in the same direction. After collision, the first, mass is stopped completely while the second one, splits into two particles each of mass ‘m’, which, move at angle 450 with respect to the original, direction., The speed of each of the moving particle will be:(a) v / (2 2), , (b), , (c) 2 v, (d) v / 2, 62. Two particles, of masses M and 2M, moving as, shown, with speeds of 10 m/s and 5 m/s, collide, elastically at the origin. After the collision, they, move along the indicated directions with speed v1, and v2, respectively. The values of v1 and v2 are, nearly:, , (a) 3.2 m/s and 6.3 m/s, (b) 3.2m/s and 12.6, m/s, (c) 6.5m/s and 6.3 m/s, (d) 6.5m/s and 3.2m/s, 63. A bag (mass M) hangs by along thread and a bullet, (mass m) comes horizontally with velocity  and, get caught in the bag. Then for the combined (bag, + bullet) system:, mM, m2, (b) Kinetic energy is, 2, Mm, m(M  m), (c) Momentum is, M, m 2 2, (d) Kinetic energy is, 2(M  m), , (a) Momentum is, , 64. A bullet of mass m moving with velocity  strikes, a block of mass M at rest and get embedded into it., The kinetic energy of the composite block will be:(a), , 1, m, m2 , 2, (m  M), , (b), , 1, M, m2 , 2, (m  M), , (c), , 1, (M  m), m2 , 2, M, , (d), , 1, m, M2 , 2, (m  M), , Elastic & Inelastic collision, Head on collision, , 4. Two equal masses m1 and m 2 moving along the same, straight line with velocities + 3 m/s and -5 m/s, respectively collide elastically. Their velocities after, the collision will be respectively, (a) +4 m/s for both, (b) - 3 m/s and +5m/s, (c) -4m/s and +m/s, (d) – 5 m/s and +, 5. A particle of mass m moving with horizontal speed 6, m/sec as shown in figure. If m << M then for one, dimensional elastic collision, the speed of lighter, particle after collision will be:-, , (a) 2m/sec in original direction, (b) 2m/sec opposite to the original direction, (c) 4m/sec opposite to the original direction, 1. A ball moving with velocity 2 m/s collides head on, (d) 4 m/sec in original direction, with another stationary ball of double the mass. If the, 6., A body falling from a height of 10 m redounds from, coefficient of restitution is 0.5, then their velocities, hard floor. If it loses 20% energy in the impact, then, (in m/s) after collision will be, coefficient of restitution is:(a) 0, 1, (b) 1, 1, (c) 1, 0.5, (d) 0, 2, (a) 0.89, (b) 0.56, (c) 0.23, (d) 0.18, 2. A metal ball of mass 2 kg moving with a velocity of, 7., Two, masses, m, and, m, moving, with, velocities A, A, B, 36 km/h has a head on collision with stationary ball of, and B in opposite direction collide elastically. After, mass 3 kg. If after the collision, the two balls move, that the masses mA and mB move with velocity B and, together, the loss in kinetic energy due to collision is, A respectively. The ratio (mA/mB)is:(a) 140 J, (b) 100 J (c) 60 J, (d) 40 J,  , 3. Two balls at same temperature collide. What is, (a) 1, (b) A B, conserved, A   B, (a)Temperature, (b) Velocity, (c) (mA + mB)/mA, (d) A/B, (c) Kinetic energy, (d) Momentum, MEDJEE CLASSES 4/641 Vijyant Khand Gomtinagar Lucknow, contact 991922289

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8. A neutron makes a head-on elastic collision with a, (c) M1 < M2, (d) Data is not sufficient to, stationary deuteron. The fractional energy loss of the, predict it, neutron in the collision is:18. Two identical balls A and B having velocities of 0.5, (a) 16/81, (b) 8/9, (c) 8/27, (d) 2/3, m/s and – 0.3 m/s respectively collide elastically in, 9. A space craft of mass ‘M’ and moving with velocity, one dimension. The velocities of B and A after the, ‘’ suddenly breaks in two pieces of same mass m., collision respectively will be, After the explosion one of the mass ‘m’ becomes, (a) 0.3 m/s and 0.5 m/s, stationary. What is the velocity of the other part of, (b) -0.5 m/s and 0.3 m/s, craft:(c) 0.5 m/s and -0.3 m/s, M, M, Mm, (d) -0.3 m/s and 0.5 m/s, , (a) (b), (c), (d), Mm, , m, , m, , 10. A ball moving with velocity 2 m/s. collides head on, with another stationary ball of double the mass. If the, coefficient of restitution is 0.5, then their velocities, (in m/s) after collision will be:(a) 0, 2, (b) 0, 1, (c) 1, 1, (d) 1, 0.5, 11. In an inelastic collision, what is conserved:(a) Kinetic energy, (b) Momentum, (c) Both (a) & (b), (d) None of these, 12. Two equal masses m1 and m2 moving along the same, straight line with velocities + 3 m/s and- 5 m/s, respectively collide elastically. Their velocities after, the collision will be respectively, (a) + 4 m s-1 for both, (b) – 3 ms-1 and + 5 ms-1, (c) – 4 m s-1 and + 4 ms-1, (d) -5 ms-1 and + 3 ms-1, 13. A ball is dropped from height h on a plane. If the, coefficient of restitution of the plane is e and if ball, hits ground two times, the height upto which it, reaches after two jumps, will be, (a) e4h, (b) eh, (c) 2eh, (d) eh/2, 14. For inelastic collision, between two spherical rigid, bodies, (a) The total kinetic energy is conserved, (b) The total potential energy is conserved, (c) The linear momentum is not conserved, (d) The linear momentum is conserved, 15. Which of the following is not an example of perfectly, inelastic collision?, (a) A bullet fired into a block if bullet gets embedded, into block, (b) Capture of electrons by an atom, (c) A man jumping into a moving boat, (d) A ball bearing striking another ball bearing, 16. Which of the following is true:, (a) Momentum is conserved in all collision but kinetic, energy is conserved only in inelastic collision, (b) Neither momentum nor kinetic energy is conserved, in inelastic collision, (c) Momentum is conserved in all collision but not, kinetic energy, (d) Both momentum and kinetic energy are conserved, in all collision., 17. A ball of mass M1 collides elastically and head-on, with another ball of mass M2 which is initially at rest., In which of the following cases the transfer of, momentum will be maximum?, (a) M1 = M2, (b) M1 > M2, , Single choice questions (Level 1), , 19. A moving block having mass m, collides with another, stationary block having mass 4m. the lighter block, comes to rest after collision. When the initial velocity, of the lighter block is v, then the value of coefficient, of restitution (e) will be, (a) 0.8, (b) 0.25, (c) 0.5, (d) 0.4, 20. A body of mass 2 kg makes an elastic collision with a, second body at ret and continues to move in the, original direction but with one fourth of its original, speed. What is the mass of the second body?, (a) 1.8 kg, (b) 1.2 kg, , (c) 1.5 kg, , (d) 1.0 kg, , Oblique collision, , 21. A billiards player hits a stationary ball by an identical, ball to pocket the target ball in a corner pocket that is, at an angle of 35o with respect to the direction of, motion of the first ball. Assuming the collision as, elastic and that friction and rotational motion are not, important, the angle made by the target ball with, respect to the incoming ball is:(a) 35o, (b) 50o, (c) 55o, (d) 60o, 22. On a frictionless surface, a block of mass M moving, at speed v collides elastically with another block of, same mass M which is initially at rest. After collision, the first block moves at an angle  to its initial, direction and has a speed, , v, . The second block’s, 3, , speed after the collision is:, , 3, 3, 2 2, 3, v, v (b), v (c) v (d), 4, 2, 3, 2, Miscellaneous Questions(LM, collision), (a), , MEDJEE CLASSES 4/641 Vijyant Khand Gomtinagar Lucknow, contact 991922289

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1. Two particles of masses m1, m2 move with initial, velocities u1 and u2. On collision, one of the particles, get excited to higher level, after absorbing energy  ., If final velocities of particles be v1 and v2 then we, must have:, (a), , 1, 1, 1, 1, m1u12  m2u22  m1v12  m2v22  , 2, 2, 2, 2, , (b), , 1, 1, 1, 1, m1u12  m22u22    m12v12  m22v22, 2, 2, 2, 2, 2, 2, 2, 2, (d) m1 u1  m2 u2    m1 v1  m2 v2, (c), , 2. Two spheres A and B of masses m1 and m2, respectively collide. A is at rest initially and B is, moving with velocity  along x-axis. After collision, , v, B has a velocity in a direction perpendicular to the, 2, original direction. The mass A moves after collision, in the direction:, , 1, 2, , (a)   tan 1   to the x-axis, (b) Same as B, (c), , to the x-axis, , (d) Opposite to the B, 3. A bomb of mass 1 kg initially at rest, explodes into, three fragments of masses in the ratio 1 : 1 : 3. The, two pieces of equal mass fly off perpendicular to each, other, each with a speed of 30 ms-1. What is the, velocity if the heavier fragment?, (a) 10 2 ms-1 at 450 with each of the other two, fragment?, (b) 10 2 ms-1 at 1350 with each of the other two, fragments, (c) 20 ms-1 at 450 with each of the other two, fragments, (d) 20 ms-1 at 1350 with each of the other two, fragments, 4. A bullet of mass 100 g moving with velocity v strikes, a wooden block of mass 1.9 kg at horizontal surface, gets embedded in it. The combined system covers a, distance 10 m on the surface. If  , , (a) mv2, , (b), , 3 2, mv (c) 2 mv2, 2, , (d) 4 mv2, , 6. A sphere of mass m, moving with velocity V, enters a, hanging bag of sand and stops. If the mass of the bag, is M and it is raised by height h, then the velocity of, the sphere will be, , M m, M, (b), 2 gh, m, m, m, m, (c), 2 gh (d), 2 gh, M m, M, (a), , 2 gh, , 7. A particle falls from a height h upon a fixed, horizontal plane and redounds. If e is the coefficient, of restitution, the total distance travelled before, rebounding has stopped is, ,  1  e2 , h, (a) , 2 ,  1 e , h  1  e2 , (c) , , 2  1  e2 , ,  1  e2 , h, (b) , 2 ,  1 e , h  1  e2 , (d) , , 2  1  e2 , , 8. A pendulum consists of a wooden bob of mass m and, of length/. A bullet of mass m1 is fired towards the, pendulum with a speed v1. The bullet emerges out of, the bob with a speed v1/3 and the bob just completes, motion along a vertical circle. Then v1 is, , m,  5 gl, m,  1, , (b), , 2  m1 ,   5 gl, 3 m , , m , (d)  1  gl, m, , (a) , , (c), , 3 m ,   5 gl, 2  m1 , , 9. Two identical B and C are in contact with each other, and the rest on a horizontal smooth surface. These are, hit head on by another identical ball A moving, initially with speed v as shown in figure. If collision, is elastic, then which of the cases are possible, , 1, for horizontal, 2, , surface then v is, , (a) 100m/s, (b) 200 m/s, (c) 300 m/s, (d) 400 m/s, 5. A body of mass (4m) s lying in x-y plane at rest. It, suddenly explodes into here pieces. Two pieces each, of mass (m) move perpendicular to each other with, equal speeds (v). The total kinetic energy generated, due to explosion is, , (a) 1 and 2, , (b) Only 2, , (c) Only 3, , (d) all 1, 2 and 3, , 10. A particle of mass 4m initially at rest explodes into, three pieces of masses m, m and 2m. Two pieces of, masses m and 2m move with equal speeds v in, opposite directions. The total kinetic energy released, in the process is:(a) Mv2, (b) 2 mv2, , (c) 3mv2, , (d) 4 mv2, , MEDJEE CLASSES 4/641 Vijyant Khand Gomtinagar Lucknow, contact 991922289