$A$ sphere of mass $0.1 \ kg$ is attached to a string of length $1 \ m$. It is released from a horizontal position and collides with another sphere of equal mass $m$ at rest. Find the kinetic energy gained by the second sphere. The collision is perfectly elastic. (in $J$)

$A$ neutron moving with velocity $u$ collides elastically with a stationary atom of mass number $A$. If the collision is head-on and the initial kinetic energy of the neutron is $E$, then the final kinetic energy of the neutron after the collision is:

$A$ ball of mass $m$ moving with speed $v$ collides elastically with an identical stationary ball which is initially at rest. After collision,the first ball moves at an angle $\theta$ to its initial direction and has speed $(v/3)$. The second ball moves in a straight line after the collision. Then,the speed of the second ball after the collision is:

$A$ smooth sphere $A$ is moving on a frictionless horizontal plane with angular speed $\omega$ and center of mass with velocity $v$. It collides elastically and head-on with an identical sphere $B$ at rest. Neglect friction everywhere. After the collision,their angular speeds are $\omega_A$ and $\omega_B$ respectively. Then

$A$ ball moving with velocity $V$ undergoes a perfectly elastic collision with an identical ball moving in the opposite direction with velocity $2V$. Taking the direction of $V$ as positive,find the velocities of both balls after the collision.

$A$ body of mass $m$ moving with velocity $v$ makes a head-on elastic collision with another body of mass $2m$ which is initially at rest. The loss of kinetic energy of the colliding body (mass $m$) is: