Two bodies $A$ and $B$ of masses $5.00 \ kg$ and $10.0 \ kg$ respectively,moving in opposite directions with velocities $4.00 \ m/s$ and $0.50 \ m/s$ respectively,make a head-on collision in free space. The force of their mutual interaction varies according to the given graph. The coefficient of restitution is

An object falls from a height of $20 \ cm$ on the surface of the Earth. If $75\%$ of its mechanical energy is lost after striking the Earth,the object will rebound to a height of ......... $cm$.

Which of the following is generally true when two particles collide?

In the figure shown,two identical balls of mass $M$ and radius $R$ each are placed in contact with each other on a frictionless horizontal surface. $A$ third ball of mass $M$ and radius $R$ is coming down vertically and has a velocity $v_0$ when it simultaneously hits the two balls and comes to rest. Then,each of the two bigger balls will move after the collision with a speed equal to:

$A$ particle of mass $m$ is at rest in a train moving with constant velocity with respect to the ground. Now,the particle is accelerated by a constant force $F_0$ acting along the direction of motion of the train for time $t_0$. $A$ girl in the train and a boy on the ground measure the work done by this force. Which of the following are $INCORRECT$?

$A$ $0.5\, kg$ ball is thrown up with an initial speed $14\, m/s$ and reaches a maximum height of $8.0\, m$. How much energy is dissipated by air drag acting on the ball during the ascent? (Take $g = 9.8\, m/s^2$)