$A$ sphere of mass $0.1\,kg$ is attached to a cord of $1\,m$ length. Starting from the height of its point of suspension,this sphere hits a block of the same mass at rest on a frictionless table. If the impact is elastic,then the kinetic energy of the block after the collision is ............. $J$.

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 $A$,will these two particles again reach the point $A$?

$A$ particle of mass $m$ collides with a heavy mass $M$ (initially at rest) elastically. After the collision, the particle returns with $4/9$ of its initial kinetic energy. The mass of the heavy object $M$ is ............... $m$.

An object $A$ of mass $20 \ kg$ and travelling at $20 \ m \ s^{-1}$ crashes into another object $B$ of mass $200 \ kg$ and travelling at $10 \ m \ s^{-1}$, in the same direction. After the collision, object $A$ bounces back in the opposite direction at a speed of $10 \ m \ s^{-1}$. The speed of the object $B$ after the collision is: (in $m \ s^{-1}$)

$A$ particle of mass $m$ is moving with a horizontal speed of $6 \, m/s$ as shown in the figure. If $m << M$,then for a one-dimensional elastic collision,the speed of the lighter particle after the collision will be:

When a moving body collides with a stationary body of $n$ times its mass,then the amount of kinetic energy transferred to the stationary body is