$A$ 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.

$A$ neutron with velocity $v$ and kinetic energy $E$ collides head-on with a stationary nucleus of mass number $A$. What is the fraction of kinetic energy lost by the neutron?

$A$ body of mass $M$ moving at speed $V_{0}$ collides elastically with a mass $m$ at rest. After the collision,the two masses move at angles $\theta_{1}$ and $\theta_{2}$ with respect to the initial direction of motion of the body of mass $M$. The largest possible value of the ratio $M/m$,for which the angles $\theta_{1}$ and $\theta_{2}$ will be equal,is:

$A$ moving particle of mass $m$ makes a head-on elastic collision with another particle of mass $2m$ which is initially at rest. The percentage loss in energy of the colliding particle on collision is close to .................. $\%$

$A$ 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:

$A$ heavy body moving with a velocity $30\, m/s$ and another small object at rest undergo an elastic collision. The latter will move with a velocity of .............. $m/s$.