Collision & Variable Mass PYQs Set 2 (PDF)

Set 2 of 4 · Questions 31-60 of 119

In the print window choose “Save as PDF”. The file prints without a web address or date line.

Mere Teacher · Previous Year Questions JEE Main Physics · Collision & Variable Mass · Set 2 (Q31-60)
Scan or visit mereteacher.com for free PYQ practice, timed CBT tests, step-by-step solutions and BroBot AI. Answers and solutions are free with a sign-up.
31. $A body of mass 3 kg moving with a velocity (2 i + 3 j + 3 k) m / s collides with another body of mass 4 kg moving with a velocity (3 i + 2 j - 3 k) m / s . The two bodies stick together after collision. The velocity of the composite body is$ (1) $\frac{1}{7} (4 i + 6 j - 3 k)$ (2) $\frac{1}{7} (18 i + 17 j - 3 k)$ (3) $\frac{1}{7} (6 i + 4 j - 6 k)$ (4) $\frac{1}{7} (9 i + 8 j - 6 k)$ 32. $Two equal masses m_{1} and m_{2} moving along the same straight line with velocities + 3 m / s and - 5 m / s respectively collide elastically. Their velocities after the collision will be respectively$ (1) $- 4 m / s and +4m/s$ (2) $+ 4 m / s for both$ (3) $- 3 m / s and + 5 m / s$ (4) $- 5 m / sand + 3 m / s .$ 33. $A metal ball of mass 2 kg moving with speed of 36 km / h has a head on collision with a stationary ball of mass 3 kg . If after collision, both the balls move as a single mass, then the loss in K.E. due to collision is$ (1) $100 J$ (2) $140 J$ (3) $40 J$ (4) $60 J.$ 34. $A body of mass m_{1} moving with an unknown velocity of v_{1} i, undergoes a collinear collision with a body of mass m_{2} moving with a velocity v_{2} i . After collision, m_{1} and m_{2} move with velocities of v_{3} i and v_{4} i, respectively. If m_{2} = 0.5 m_{1} and v_{3} = 0.5 v_{1}, then v_{1} is:$ (1) $\frac{v _{4} - v _{2}}{2}$ (2) $v_{4} - v_{2}$ (3) $\frac{v _{4} - v _{2}}{4}$ (4) $v_{4} + v_{2}$ 35. $A billiard ball of mass M, moving with velocity v_{1} collides with another ball of the same mass but at rest. If the collision is elastic, the angle of divergence after the collision is$ (1) $0^{\circ}$ (2) $30^{\circ}$ (3) $90^{\circ}$ (4) $45^{\circ}$ 36. $Two identical balls A and B having velocities of 0.5 m / s and - 0.3 m / s respectively collide elastically in one-dimension. The velocities of B and A after the collision respectively will be [NEET 2016]$ (1) $- 0.5 m / s and 0.3 m / s$ (2) $0.5 m / s and - 0.3 m / s$ (3) $- 0.3 m / s and 0.5 m / s$ (4) $0.3 m / s and 0.5 m / s$ 37. $A block of mass 1.9 kg is at rest at the edge of a table, of height 1m. A bullet of mass 0.1 kg collides with the block and sticks to it. If the velocity of the bullet is 20 m / s in the horizontal direction just before the collision then the kinetic energy just before the combined system strikes the floor, is [Take g = 10 m / s^{2} . Assume there is no rotational motion and loss of energy after the collision is negligable.]$ (1) $19 J$ (2) $23 J$ (3) $20 J$ (4) $21 J$ 38. $A ball of mass 0.15 kg hits the wall with its initial speed of 12 m s^{- 1} and bounces back without changing its initial speed. If the force applied by the wall on the ball during the contact is 100 N. calculate the time duration of the contact of ball with the wall.$ (1) $0.018s$ (2) $0.036s$ (3) $0.009 s$ (4) $0.072 s$ 39. $A particle of mass ’ m^{’} is moving with speed 2 v and collides with a mass ’ 2 m^{’} moving with speed ’ v^{’} in the same direction. After collision, the first mass is stopped completely while the second one splits into two particles each of mass ’ m^{’}, which move at angle 45° with respect to the original direction. The speed of each of the moving particle will be:$ (1) $2 v$ (2) $22 v$ (3) $\frac{v}{( 2 2 )}$ (4) $\frac{v}{2}$ 40. $Two identical balls A and B having velocities of 0.5 m s^{- 1} and - 0.3 m s^{- 1} respectively collide elastically in one dimension. The velocities of B and A after the collision respectively will be (NEET‐II2016, 1994, 1991)$ (1) $- 0.5 m s^{- 1} and 0.3 m s^{- 1}$ (2) $0.5 m s^{- 1} and -0.3 m s^{- 1}$ (3) $-0.3 m s^{- 1} and 0.5 m s^{- 1}$ (4) $0.3 m s^{- 1} and 0.5 m s^{- 1}$ 41. $A body falls freely from a height ' h' on a fixed horizontal plane and rebounds. If 'e' is the coefficient of restitution, the total distance travelled before it comes to rest is$ (1) $h (\frac{1 + e ^{2}}{1 - e ^{2}})$ (2) $h (\frac{1 - e ^{2}}{1 + e ^{2}})$ (3) $\frac{h}{2} (\frac{1 - e ^{2}}{1 + e ^{2}})$ (4) $\frac{h}{2} (\frac{1 + e ^{2}}{1 - e ^{2}})$ 42. $A ball moving with velocity 2 m / s collides head on with another stationary ball of double the mass. If the coefficient of restitution is 0.5, then their velocities (in m / s) after collision will be$ (1) $0,1$ (2) $1,1$ (3) $1,0.5$ (4) $0,2$ 43. $A liquid of density ρ is coming out of a hose pipe of radius a with horizontal speed v and hits a mesh. 50 % of the liquid passes through the mesh unaffected. 25% loses all of its momentum and 25 % comes back with the same speed. The resultant pressure on the mesh will be:$ (1) $\frac{1}{4} ρ v^{2}$ (2) $\frac{3}{4} ρ v^{2}$ (3) $\frac{1}{2} ρ v^{2}$ (4) $ρ V^{2}$ 44. $A bouncing ball of mass 200 g falls from the height of 5 m on a horizontal ground. After every impact with the ground, the velocity of the ball decreases by \frac{1}{2} times. The total momentum, the ball imparts on to the ground after 3 impacts is (Let g = 10 m / s^{2})$ (1) $\frac{14}{4} kg m / s$ (2) $\frac{20}{6} kg m / s$ (3) $\frac{26}{12} kg m / s$ (4) $\frac{21}{4} kg m / s$ 45. $A metal ball of mass 2 kg moving with a velocity of 36 km / h has a head on collision with a stationary ball of mass 3 kg . After the collision, if both balls move together, then the loss in kinetic energy due to collision is$ (1) $40 J$ (2) $60 J$ (3) $100 J$ (4) $140 J$ 46. $Two particles of equal mass m have respective initial velocities u i^and u (\frac{i + j}{2}) . They collide completely inelastically. The energy lost in the process is:$ (1) $\frac{m v ^{2}}{8}$ (2) $\frac{5 m v ^{2}}{8}$ (3) $\frac{m v ^{2}}{4}$ (4) $\frac{3 v m ^{2}}{8}$ 47. $100 balls each of mass m moving with speed v simultaneously strike a wall normally and reflected back with same speed, in time t s. The total force exerted by the balls on the wall is$ (1) $\frac{100 m v}{t}$ (2) $\frac{200 m v}{t}$ (3) $200 mvt$ (4) $\frac{m v}{100 t}$ 48. $A block of mass 4 m traveling at a velocity v_{1} in x -direction on a frictionless horizontal plane make a head-on collision with another block of mass 2 m travelling in opposite direction with a velocity v_{2} . After collision, both the blocks travel as a single block along x -direction with a final velocity 5 v_{2} . The ratio of velocity \frac{v _{1}}{v _{2}} is$ (1) $2$ (2) $3$ (3) $5$ (4) $8$ 49. $Two blocks of masses 10 kg and 30 kg are placed on the same straight line with coordinates (0, 0) cm and (x, 0) cm respectively. The block of 10 kg is moved on the same line through a distance of 6 cm towards the other block. The distance through which the block of 30 kg must be moved to keep the position of center of mass of the system unchanged is:$ (1) $4 cm towards the 10 kg block$ (2) $2 cm away from the 10 kg block$ (3) $2 cm towards the 10 kg block$ (4) $4 cm away from the 10 kg block$ 50. $Two small particles of equal masses start moving in opposite directions from a point A in a horizontal circular orbit. Their tangential velocities are v and 2v, respectively, as shown in the figure. Between collisions, the particles move with constant speeds. After making how many elastic collisions, other than that at A, these two particles will again reach the point A?$ (1) $4$ (2) $3$ (3) $2$ (4) $1$ 51. $A tennis ball is dropped on a horizontal smooth surface. It bounces back to its original position after hitting the surface. The force on the ball during the collision is proportional to the length of compression of the ball. Which one of the following sketches describes the variation of its kinetic energy K with time t most appropriately? The figures are only illustrative and not to the scale.$ (1) (2) (3) (4) 52. $A circular hole of radius (\frac{a}{2}) is cut out of a circular disc of radius 'a' shown in figure. The centroid of the remaining circular portion with respect to point O^{’} will be:$ (1) $\frac{10}{11} a$ (2) $\frac{2}{3} a$ (3) $\frac{1}{6} a$ (4) $\frac{5}{6} a$ 53. $Three-point particles of masses 1.0 kg, 1.5 kg and 2.5 kg are placed at three corners of a right-angle triangle of sides 4.0 cm, 3.0 cm and 5.0 cm as shown in the figure. The center of mass of the system is at a point:$ (1) $0.6 cm to the right and 2 cm above 1 kg mass$ (2) $0.9 cm to the right and 2 cm above 1 kg mass$ (3) $0.9 cm to the left and 2 cm above 1 kg mass$ (4) $0.9 cmto the right and 1.5 cm above 1 kg mass$ 54. $Two particles P and Q each of mass 3 m lie at rest on the X -axis at points (- a, 0) and (+ a, 0), respectively. A third particle R of mass 2 m initially at the origin moves towards the particle Q . If all the collisions of the system of 3 particles are elastic and head on, the total number of collisions in the system is$ (1) $2$ (2) $3$ (3) $4$ (4) $5$ 55. $Find the coordinates of centre of mass of the lamina, shown in figure.$ (1) $0.75, 1.75$ (2) $0.75, 1.5$ (3) $0.5, 1.75$ (4) $0.5, 1.5$ 56. $An object of mass m_{1} collides with another object of mass m_{2} which is at rest. After the collision the objects move with equal speeds in opposite direction. The ratio of the masses m_{2} : m_{1} is:$ (1) $3:1$ (2) $2:1$ (3) $1:2$ (4) $1:1$ 57. $A ball of mass 4 kg, moving with a velocity of 10 ms^{- 1} collides with a spring of length 8 m and force constant 100 Nm^{- 1} . The length of the compressed spring is xm . The value of X, to the nearest integer, is____$ 58. $A ball is dropped from a height of 20 m. If the coefficient of restitution for the collision between ball and floor is 0.5, after hitting the floor, the ball rebounds to a height of_________m.$ 59. $A solid circular disc of mass 50 kg rolls along a horizontal floor so that its center of mass has a speed of 0.4 m / s . The absolute value of work done on the disc to stop it is J.$ 60. $A body having specific charge 8 μ C / g is resting on a frictionless plane at a distance 10cm from the wall (as shown in the figure). It starts moving towards the wall when a uniform electric field of 100V/m is applied horizontally towards the wall. If the collision of the body with the wall is perfectly elastic, then the time period of the motion will be ___ s.$