$A$ body of mass $m$ moving with velocity $v$ collides with a stationary body of mass $2m$. The fraction of kinetic energy lost by the body of mass $m$ is:

On a horizontal smooth surface,a disc of radius $r$ is placed at rest. Another disc of the same mass is moving towards it with an impact parameter equal to its own radius. What should be the radius of the incoming disc so that after the collision,the first disc moves at an angle of $45^{\circ}$ to the direction of motion of the incoming disc?

$A$ particle of mass $1\, kg$ moving with velocity $1\, m/s$,collides elastically with another particle of mass $m$ initially at rest. In the collision,the particle of mass $1\, kg$ loses $\frac{3}{4}$ of its kinetic energy $(K.E.)$. The value of $m$ is:

Two smooth objects with a coefficient of restitution $e$ collide directly and bounce as shown. Newton's law of restitution gives:

$A$ ball of mass $m$ moving with velocity $v$ undergoes an elastic collision with another ball of the same mass $m$ moving in the opposite direction with velocity $2v$. What will be their velocities after the collision?

$A$ ball falls from a height of $5\,m$ and strikes the roof of a lift. If at the time of collision,the lift is moving in the upward direction with a velocity of $1\,m/s$,then the velocity with which the ball rebounds after collision will be (assume $e = 1$):