Collision & Variable Mass PYQs Set 4 (PDF)

Set 4 of 4 · Questions 91-119 of 119

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Mere Teacher · Previous Year Questions JEE Main Physics · Collision & Variable Mass · Set 4 (Q91-119)
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91. $A simple pendulum of length 1 m has a wooden bob of mass 1 kg . It is struck by a bullet of mass 10^{- 2} kg moving with a speed of 2 \times 10^{2} ms^{- 1} . The bullet gets embedded into the bob. The height to which the bob rises before swinging back is. (use g = 10 \frac{m}{s ^{2}})$ (1) $0.30 m$ (2) $0.20 m$ (3) $0.35 m$ (4) $0.40 m$ 92. $A rod of length L has non-uniform linear mass density given by ρ (x) = a + b (\frac{x}{L})^{2} where a and b are constants and 0 \leq x \leq L . The value of x for the centre of mass of the rod is at:$ (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) $\frac{3}{2} (\frac{a + b}{2 a + b}) L$ 93. $Three objects A, B and C are kept in a straight line on a frictionless horizontal surface. The masses of A, B and C are m, 2m and 2m respectively. A moves towards B with a speed of 9m/s and makes an elastic collision with it. Thereafter B makes a completely inelastic collision with C. All motions occur along same straight line. The final speed of C is:$ (1) $6m/s$ (2) $9m/s$ (3) $4m/s$ (4) $3m/s$ 94. $Two particles, of masses M and 2M, moving, as shown, with speeds of 10 m/s and 5 m/s, collide elastically at the origin. After the collision, they move along the indicated directions with speeds v_{1} and v_{2} respectively. The values of v_{1} and v_{2} are nearly:$ (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) $3.2 m/s and 12.6 m/s$ 95. $What percentage of kinetic energy of a moving particle is transferred to a stationary particle when it strikes the stationary particle of 5 times its mass? (Assume the collision to be head-on elastic collision)$ (1) $50.0%$ (2) $66.6%$ (3) $55.5%$ (4) $33.3%$ 96. $An alpha -particle of mass m suffers 1-dimensional elastic collision with a nucleus at rest of unknown mass. It is scattered directly backwards losing, 64 % of its initial kinetic energy. The mass of the nucleus is:$ (1) $2m$ (2) $3.5 m$ (3) $1.5 m$ (4) $4 m$ 97. $The position vector of the centre of mass r_{cm} of an asymmetric uniform bar of negligible area of cross- section as shown in figure is -$ (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) $r cm = \frac{11}{8} Lx + \frac{3}{8} L y$ 98. $Two balls X (2 kg) and Y (4 kg) approach each other with equal speeds of 10 ms^{- 1} . If the collision is perfectly elastic, then the new velocities of balls X and Y are respectively$ (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) $\frac{50}{3} m s^{- 1}, \frac{10}{3} m s^{- 1}$ 99. $Two spheres A and B of masses m_{1} and m_{2} respectively collide. A is at rest initially and B is moving with velocity v along x ‐axis. After collision B has a velocity in a direction perpendicular to the original direction. The mass A moves after collision in the direction$ (1) $same as that of B$ (2) $opposite to that of B$ (3) $Θ = tan^{- 1} (\frac{1}{2}) to the x‐axis$ (4) $Θ = tan^{- 1} (- \frac{1}{2}) to the x‐axis (2012)$ 100. $A simple pendulum, made of a string of length l and a bob of mass m, is released from a small angle θ_{0} . It strikes a block of mass M, kept on a horizontal surface at its lowest point of oscillations, elastically. It bounces back and goes up to an angle θ_{1} . The M is given by:$ (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) $\frac{m}{2} (\frac{θ _{0} - θ _{1}}{θ _{0} + θ _{1}})$ 101. $Body of mass moving with speed collides with another body of mass , at rest. The collision is head-on and elastic in nature. After the collision, the fraction of energy lost by the colliding body is [NEET 2019]$ (1) $\frac{8}{9}$ (2) $\frac{4}{9}$ (3) $\frac{5}{9}$ (4) $\frac{1}{9}$ 102. $In a perfectly inelastic collision, two spheres made of the same material with masses 15 kg and 25 kg, moving in opposite directions with speeds of 10 m / s and 30 m / s, respectively, strike each other and stick together. The rise in temperature (in^{\circ} C), if all the heat produced during the collision is retained by these spheres, is : (specific heat of sphere material 31 cal / kg .^{\circ} C and 1 cal = 4.2 J)$ (1) $1.15$ (2) $1.75$ (3) $1.44$ (4) $1.95$ 103. $A point particle of mass m, moves along the uniformly rough track PQR as shown in the figure. The coefficient of friction, between the particle and the rough track equals µ. The particle is released, from rest, from the point P and it comes to rest at a point R. The energies, lost by the ball, over the parts, PQ and QR, of the track, are equal to each other, and no energy is lost when particle changes direction from PQ to QR. The values of the coefficient of friction µ and the distance x (= QR), are, respectively close to:$ (1) $0.2 and 3.5 m$ (2) $0.29 and 3.5 m$ (3) $0.29 and 6.5 m$ (4) $0.2 and 6.5 m$ 104. $Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): Three identical spheres of same mass undergo one dimensional motion as shown in figure with initial velocities v_{A} = 5 m / s, v_{B} = 2 m / s, v_{C} = 4 m / s . If we wait sufficiently long for elastic collision to happen, then v_{A} = 4 m / s, v_{B} = 2 m / s, v_{C} = 5 m / s will be the final velocities. Reason (R): In an elastic collision between identical masses, two objects exchange their velocities. choose the correct answer from the options given below:$ (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) $(A) is true but (R) is false$ 105. $A box of mass 3 kg moves on a horizontal frictionless table and collides with another box of mass 3 kg initially at rest on the edge of the table at height 1 m . The speed of the moving box just before the collision is 4 m / s . The two boxes stick together and fall from the table. The kinetic energy just before the boxes strike the floor is (Assume, acceleration due to gravity, g = 10 m / s^{2})$ (1) $40 J$ (2) $80 J$ (3) $96 J$ (4) $72 J$ 106. $Particle A of mass m_{1} moving with velocity (3 i^+ j^) m s^{- 1} collides with another particle B of mass m_{2} which is at rest initially. Let V \to_{1} and V \to_{2} be the velocities of particles A and B after collision respectively. If m_{1} = 2 m_{2} and after collision v \to_{1} = (i^+ 3 j^) ms^{- 1} the angle between v \to_{1} and v \to_{2} is$ (1) $- 45^{o}$ (2) $60 °$ (3) $15 °$ (4) $105^{o}$ 107. $The velocity of the bullet becomes one third after it penetrates 4 cm in a wooden block. Assuming that bullet is facing a constant resistance during its motion in the block. The bullet stops completely after travelling at (4 + x) cm inside the block. The value of x is:$ (1) $2.0$ (2) $1.0$ (3) $0. 5$ (4) $1.5$ 108. $A block of mass 0.50 kg is moving with a speed of 2.00 m s^{-1} on a smooth surface. It strikes another mass of 1.00 kg and then they move together as a single body. The energy loss during the collision is :$ (1) $1.00 J$ (2) $0.67 J$ (3) $0.34 J$ (4) $0.16 J$ 109. $During inelastic collision between two objects, which of the following quantity always remains conserved?$ (1) $Total linear momentum$ (2) $Total kinetic energy$ (3) $Speed of each body$ (4) $Total mechanical energy$ 110. $A ball of mass 200 g rests on a vertical post of height 20 m. A bullet of mass 10 g, travelling in horizontal direction, hits the center of the ball After collision both travels independently. The ball hits the ground at a distance 30 m and the bullet at a distance of 120 m from the foot of the post. The value of initial velocity of the bullet will be (if g= 10 m/ s^{2}):$ (1) $120 m/s$ (2) $60 m/s$ (3) $400 m/s$ (4) $360 m/s$ 111. $A body of mass 1 kg collides head on elastically with a stationary body of mass 3 kg. After collision, the smaller body reverses its direction of motion and moves with a speed of 2m/s. The initial speed of the smaller body before collision is _______m s^{- 1} .$ 112. $A uniform rod AB of mass 2 kg and Length 30 cm at rest on a smooth horizontal surface. An impulse of force 0.2 Ns is applied to end B . The time taken by the rod to turn through at right angles will be \frac{π}{x} s, where x =______$ 113. $The position of the centre of mass of a uniform semi-circular wire of radius 'R' placed in x-y plane with its centre at the origin and the line joining its ends as x-axis is given by (0, \frac{x R}{π}) . Then, the value of \|x\| is ______$ 114. $A nucleus disintegrates into two smaller parts, which have their velocities in the ratio 3:2. The ratio of their nuclear sizes will be (\frac{x}{3})^{\frac{1}{3}} . The value of 'x' is:$ 115. $A batsman hits back a ball of mass 0.4 kg straight in the direction of the bowler without changing its initial speed of 15 m s^{- 1} . The impulse imparted to the bal1 is________Ns.$ 116. $A ball of mass 10 kg moving with a velocity 103 m/s along the x-axis, hits another ball of mass 20 kg which is at rest. After the collision, first ball comes to rest while the second ball disintegrates into two equal pieces. One piece starts moving along y-axis with a speed of 10 m/s. The second piece starts moving at an angle of 30° with respect to the x-axis. The velocity of the ball moving at 30° with x-axis is x m/s. The configuration of pieces after collision is shown in the figure below. The value of x to the nearest integer is:$ 117. $A ball of mass 10 kg moving with a velocity 103 ms^{- 1} along X-axis, hits another ball of mass20kg whichis at rest. After collision, the first ball comes to rest and the second one disintegrates into two equal pieces. One of the pieces starts moving along Y-axis at a speed of 10 m/s. The second piece starts moving at a speed of 20 m/s at an angle θ (degree) with respect to the X-axis. The configuration of pieces after collision is shown in the figure. The value of θ to the nearest integer is _________.$ 118. $A pendulum of length 2 m consists of a wooden bob of mass 50 g. A bullet of mass 75 g is fired towards the stationary bob with a speed v. The bullet emerges out of the bob with a speed \frac{v}{3} and the bob just completes the vertical circle. The value of v is________m s^{- 1} . (if g = 10 m/ s^{2})$ 119. $The distance of center of mass from end A of a one-dimensional rod (AB) having mass density ρ = ρ_{0} (1 - \frac{x ^{2}}{L ^{2}}) kg / m and length L (in meter) is \frac{3 L}{α} m . The value of α is .......... (where x is the distance form end A)$