$A$ uniform rod of mass $M$ and length $L$ is placed on a smooth horizontal surface. $A$ particle of mass $m$ moving with velocity $v$ strikes the rod at one end perpendicularly and comes to rest. The velocity of the centre of mass of the rod after the collision is:

$A$ ball of mass $m$ is thrown at a wall with speed $v$ at an angle $\theta$ with the normal to the wall. If the coefficient of restitution is $e$,what will be the magnitude and direction of the velocity of the ball after the collision with respect to the wall?

$A$ $2\, kg$ block moving with $10\, m/s$ strikes a spring of constant $\pi^2\, N/m$ attached to a $2\, kg$ block at rest kept on a smooth floor. The velocity of the rear $2\, kg$ block after it separates from the spring will be ..... $m/s$.

If $n$ balls hit elastically and normally on a surface per unit time and all balls of mass $m$ are moving with the same velocity $u$, then the force on the surface is ..........

$A$ ball of mass $1 \ kg$ moving along the $X$-direction collides elastically with a stationary ball of mass $m$. The first ball (mass $= 1 \ kg$) recoils at a right angle to its original direction of motion. If the second ball starts moving at an angle $30^{\circ}$ with the $X$-axis,the value of $m$ must be (in $kg$)

$A$ body $A$ of mass $4m$ moving with speed $u$ collides with another body $B$ of mass $2m$,which is at rest. The collision is head-on and elastic in nature. After the collision,the fraction of energy lost by the colliding body $A$ is