Collision & Variable Mass PYQs Set 3 (PDF)

Set 3 of 4 · Questions 61-90 of 93

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Mere Teacher · Previous Year Questions NEET Physics · Collision & Variable Mass · Set 3 (Q61-90)
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61. $A body of mass M moving at speed V_{0} collides elastically with a mass 'm' at rest. After the collision, the two masses move at angles θ_{1} and θ_{2} with respect to the initial direction of motion of the body of mass M. The largest possible value of the ratio M/m, for which the angles θ_{1} and θ_{2} will be equal, is:$ (1) $4$ (2) $1$ (3) $3$ (4) $2$ 62. $A mass m moving horizontally (along the x ‐axis) with velocity v collides and sticks to a mass of 3 m moving vertically upward (along the y ‐axis) with velocity 2 v . The final velocity of the combination is (Mains 2011)$ (1) $\frac{3}{2} v i + \frac{1}{4} v j$ (2) $\frac{1}{4} v i + \frac{3}{2} v j$ (3) $\frac{1}{3} v i + \frac{2}{3} v j$ (4) $\frac{2}{3} v i + \frac{1}{3} v j$ 63. $A piece of wood of mass 0.03 kg is dropped from the top of a 100 m height building. At the same time, a bullet of mass 0.02 kg is fired vertically upward, with a velocity 100 m s^{- 1}, from the ground. The bullet gets embedded in the wood. Then the maximum height of which the combined system reaches above the top of the building before falling below is: (g = 10 m s^{- 2})$ (1) $20 m$ (2) $30 m$ (3) $40 m$ (4) $10 m$ 64. $Four particles A, B, C and D with masses m_{A} = m, m_{B} = 2 m, m_{C} = 3 m and m_{D} = 4 m are at the corners of a square. They have accelerations of equal magnitude with directions as shown. The acceleration of the centre of mass of the particles is:$ (1) $\frac{a}{5} (i - j)$ (2) $a (i - j)$ (3) $Zero$ (4) $a10i-j$ 65. $As per the given figure, a small ball P slides down the quadrant of a circle and hits the other ball Q of equal mass which is initially at rest. Neglecting the effect of friction and assume the collision to be elastic, the velocity of ball Q after collision will be: (g = 10 m/ s^{2})$ (1) $0$ (2) $0.25 m/s$ (3) $2 m/s$ (4) $4 m/s$ 66. $There block, A, B and C are lying on a smooth horizontal surface, as shown in figure. A and B have equal masses, m while C has mass M . A is a given an initial speed v towards B due to which it collides with B perfectly inelastically. The combined mass collides with C, also perfectly inelastically \frac{5}{6} th of the kinetic energy is lost in whole process. What is value of M/m?$ (1) $5$ (2) $2$ (3) $4$ (4) $3$ 67. $Two bodies A and B of same mass undergo completely inelastic one-dimensional collision. The body A moves with velocity v_{1} while body B is at rest before collision. The velocity of the system after collision is v_{2} . The ratio v_{1} : v_{2} is [NEET 2024]$ (1) $1 : 2$ (2) $2 : 1$ (3) $4 : 1$ (4) $1 : 4$ 68. $Blocks of masses m, 2 m, 4 m and 8 m are arranged in a line on a frictionless floor. Another block of mass m, moving with speed v along the same line (see figure) collides with mass m in perfectly inelastic manner. All the subsequent collisions are also perfectly inelastic. By the time the last block of mass 8 m starts moving the total energy loss is p% of the original energy. Value of 'P' is close to$ (1) $37$ (2) $77$ (3) $87$ (4) $94$ 69. $A particle of mass m, moving with a velocity v makes an elastic collision in one dimension with a stationary particle of mass m . During the collision, they remain in contact with each other for an extremely small time T . Their force of contact, with time is shown in the figure. Then, F_{0}$ (1) $\frac{2 mv}{T}$ (2) $\frac{4 mv}{3 T}$ (3) $\frac{mv}{T}$ (4) $\frac{3 mv}{4 T}$ 70. $Two billiard balls of mass 0.05 kg each moving in opposite directions with 10 m s^{- 1} collide and rebound with the same speed. If the time duration of contact is t = 0.005 s, then what is the force exerted on the ball due to each other?$ (1) $100 N$ (2) $200 N$ (3) $300 N$ (4) $400 N$ 71. $A particle of mass m moving in the x direction with speed 2v is hit by another particle of mass 2m moving in the y direction with speed v. If the collision is perfectly inelastic, the percentage loss in the energy during the collision is close to :$ (1) $44%$ (2) $50%$ (3) $56%$ (4) $62%$ 72. $As shown in figure. When a spherical cavity (centered at O) of radius 1 is cut out of a uniform sphere of radius R (centered at C), the centre of mass of remaining (shaded) part of sphere is at G, i.e on the surface of the cavity. R can be determined by the equation:$ (1) $(R^{2} + R + 1) (2 - R) = 1$ (2) $(R^{2} - R - 1) (2 - R) = 1$ (3) $(R^{2} - R + 1) (2 - R) = 1$ (4) $(R^{2} + R - 1) (2 - R) = 1$ 73. $A particle of mass m is projected with a speed u from the ground at an angle θ = π /3 w.r.t. horizontal (x -axis). When it has reached its maximum height, it collides completely in-elastically with another particle of the same mass and velocity u i^. The horizontal distance covered by the combined mass before reaching the ground is:$ (1) $\frac{3 3}{8} \frac{u ^{2}}{g}$ (2) $22 \frac{u ^{2}}{g}$ (3) $\frac{5}{8} \frac{u ^{2}}{g}$ (4) $\frac{3 2}{4} \frac{u ^{2}}{g}$ 74. $A simple pendulum of length 1 m has a wooden bob of mass 1 kg . It is struck by a bullet of mass 10^{- 2} kg moving with a speed of 2 \times 10^{2} ms^{- 1} . The bullet gets embedded into the bob. The height to which the bob rises before swinging back is. (use g = 10 \frac{m}{s ^{2}})$ (1) $0.30 m$ (2) $0.20 m$ (3) $0.35 m$ (4) $0.40 m$ 75. $A rod of length L has non-uniform linear mass density given by ρ (x) = a + b (\frac{x}{L})^{2} where a and b are constants and 0 \leq x \leq L . The value of x for the centre of mass of the rod is at:$ (1) $\frac{4}{3} (\frac{a + b}{2 a + 3 b}) L$ (2) $\frac{3}{4} (\frac{2 a + b}{3 a + b}) L$ (3) $\frac{3}{2} (\frac{2 a + b}{3 a + b}) L$ (4) $\frac{3}{2} (\frac{a + b}{2 a + b}) L$ 76. $Three objects A, B and C are kept in a straight line on a frictionless horizontal surface. The masses of A, B and C are m, 2m and 2m respectively. A moves towards B with a speed of 9m/s and makes an elastic collision with it. Thereafter B makes a completely inelastic collision with C. All motions occur along same straight line. The final speed of C is:$ (1) $6m/s$ (2) $9m/s$ (3) $4m/s$ (4) $3m/s$ 77. $Two particles, of masses M and 2M, moving, as shown, with speeds of 10 m/s and 5 m/s, collide elastically at the origin. After the collision, they move along the indicated directions with speeds v_{1} and v_{2} respectively. The values of v_{1} and v_{2} are nearly:$ (1) $6.5 m/s and 6.3 m/s$ (2) $3.2 m/s and 3.6 m/s$ (3) $6.5 m/s and 3.2 m/s$ (4) $3.2 m/s and 12.6 m/s$ 78. $What percentage of kinetic energy of a moving particle is transferred to a stationary particle when it strikes the stationary particle of 5 times its mass? (Assume the collision to be head-on elastic collision)$ (1) $50.0%$ (2) $66.6%$ (3) $55.5%$ (4) $33.3%$ 79. $An alpha -particle of mass m suffers 1-dimensional elastic collision with a nucleus at rest of unknown mass. It is scattered directly backwards losing, 64 % of its initial kinetic energy. The mass of the nucleus is:$ (1) $2m$ (2) $3.5 m$ (3) $1.5 m$ (4) $4 m$ 80. $The position vector of the centre of mass r_{cm} of an asymmetric uniform bar of negligible area of cross- section as shown in figure is -$ (1) $r cm = \frac{13}{8} Lx + \frac{5}{8} L y$ (2) $r cm = \frac{5}{8} Lx + \frac{13}{8} L y$ (3) $r cm = \frac{3}{8} Lx + \frac{11}{8} L y$ (4) $r cm = \frac{11}{8} Lx + \frac{3}{8} L y$ 81. $Two balls X (2 kg) and Y (4 kg) approach each other with equal speeds of 10 ms^{- 1} . If the collision is perfectly elastic, then the new velocities of balls X and Y are respectively$ (1) $\frac{50}{3} m s^{- 1}, - \frac{10}{3} m s^{- 1}$ (2) $- \frac{50}{3} m s^{- 1}, - \frac{10}{3} m s^{- 1}$ (3) $- \frac{50}{3} m s^{- 1}, \frac{10}{3} m s^{- 1}$ (4) $\frac{50}{3} m s^{- 1}, \frac{10}{3} m s^{- 1}$ 82. $Two spheres A and B of masses m_{1} and m_{2} respectively collide. A is at rest initially and B is moving with velocity v along x ‐axis. After collision B has a velocity in a direction perpendicular to the original direction. The mass A moves after collision in the direction$ (1) $same as that of B$ (2) $opposite to that of B$ (3) $Θ = tan^{- 1} (\frac{1}{2}) to the x‐axis$ (4) $Θ = tan^{- 1} (- \frac{1}{2}) to the x‐axis (2012)$ 83. $A simple pendulum, made of a string of length l and a bob of mass m, is released from a small angle θ_{0} . It strikes a block of mass M, kept on a horizontal surface at its lowest point of oscillations, elastically. It bounces back and goes up to an angle θ_{1} . The M is given by:$ (1) $\frac{m}{2} (\frac{θ _{0} + θ _{1}}{θ _{0} - θ _{1}})$ (2) $m (\frac{θ _{0} - θ _{1}}{θ _{0} + θ _{1}})$ (3) $m (\frac{θ _{0} + θ _{1}}{θ _{0} - θ _{1}})$ (4) $\frac{m}{2} (\frac{θ _{0} - θ _{1}}{θ _{0} + θ _{1}})$ 84. $Body of mass moving with speed collides with another body of mass , at rest. The collision is head-on and elastic in nature. After the collision, the fraction of energy lost by the colliding body is [NEET 2019]$ (1) $\frac{8}{9}$ (2) $\frac{4}{9}$ (3) $\frac{5}{9}$ (4) $\frac{1}{9}$ 85. $In a perfectly inelastic collision, two spheres made of the same material with masses 15 kg and 25 kg, moving in opposite directions with speeds of 10 m / s and 30 m / s, respectively, strike each other and stick together. The rise in temperature (in^{\circ} C), if all the heat produced during the collision is retained by these spheres, is : (specific heat of sphere material 31 cal / kg .^{\circ} C and 1 cal = 4.2 J)$ (1) $1.15$ (2) $1.75$ (3) $1.44$ (4) $1.95$ 86. $A point particle of mass m, moves along the uniformly rough track PQR as shown in the figure. The coefficient of friction, between the particle and the rough track equals µ. The particle is released, from rest, from the point P and it comes to rest at a point R. The energies, lost by the ball, over the parts, PQ and QR, of the track, are equal to each other, and no energy is lost when particle changes direction from PQ to QR. The values of the coefficient of friction µ and the distance x (= QR), are, respectively close to:$ (1) $0.2 and 3.5 m$ (2) $0.29 and 3.5 m$ (3) $0.29 and 6.5 m$ (4) $0.2 and 6.5 m$ 87. $Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): Three identical spheres of same mass undergo one dimensional motion as shown in figure with initial velocities v_{A} = 5 m / s, v_{B} = 2 m / s, v_{C} = 4 m / s . If we wait sufficiently long for elastic collision to happen, then v_{A} = 4 m / s, v_{B} = 2 m / s, v_{C} = 5 m / s will be the final velocities. Reason (R): In an elastic collision between identical masses, two objects exchange their velocities. choose the correct answer from the options given below:$ (1) $(A) is false but (R) is true$ (2) $Both (A) and (R) are true but (R) is NOT the correct explanation of (A)$ (3) $Both (A) and (R) are true and (R) is the correct explanation of (A)$ (4) $(A) is true but (R) is false$ 88. $A box of mass 3 kg moves on a horizontal frictionless table and collides with another box of mass 3 kg initially at rest on the edge of the table at height 1 m . The speed of the moving box just before the collision is 4 m / s . The two boxes stick together and fall from the table. The kinetic energy just before the boxes strike the floor is (Assume, acceleration due to gravity, g = 10 m / s^{2})$ (1) $40 J$ (2) $80 J$ (3) $96 J$ (4) $72 J$ 89. $Particle A of mass m_{1} moving with velocity (3 i^+ j^) m s^{- 1} collides with another particle B of mass m_{2} which is at rest initially. Let V \to_{1} and V \to_{2} be the velocities of particles A and B after collision respectively. If m_{1} = 2 m_{2} and after collision v \to_{1} = (i^+ 3 j^) ms^{- 1} the angle between v \to_{1} and v \to_{2} is$ (1) $- 45^{o}$ (2) $60 °$ (3) $15 °$ (4) $105^{o}$ 90. $The velocity of the bullet becomes one third after it penetrates 4 cm in a wooden block. Assuming that bullet is facing a constant resistance during its motion in the block. The bullet stops completely after travelling at (4 + x) cm inside the block. The value of x is:$ (1) $2.0$ (2) $1.0$ (3) $0. 5$ (4) $1.5$