An object of mass $m_{1}$ collides with another object of mass $m_{2}$,which is at rest. After the collision,the objects move with equal speeds in opposite directions. The ratio of the masses $m_{2} : m_{1}$ is

$A$ ball $A$ of mass $m$ moving along the positive $x$-direction with kinetic energy $K$ and momentum $p$ undergoes an elastic head-on collision with a stationary ball $B$ of mass $M$. After the collision,the ball $A$ moves along the negative $x$-direction with kinetic energy $K/9$. The final momentum of $B$ is:

$A$ block having mass $m$ collides with another stationary block having mass $2m$. The lighter block comes to rest after the collision. If the initial velocity of the first block is $v$,then the value of the coefficient of restitution must be:

$A$ 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

$A$ heavy body moving with a velocity of $6\,ms^{-1}$ collides elastically with a light body (whose mass is half of the mass of the heavy body) at rest. The velocity of the light body will be (in $ms^{-1}$):

Collision takes place between two solid spheres denoted as $1$ and $2$. The initial velocities of the spheres are $u_1 = 3 \ m/s$ and $u_2 = 1.5 \ m/s$,and the final velocities are $v_1 = 2.5 \ m/s$ and $v_2 = 3.5 \ m/s$. The coefficient of restitution between the materials of the spheres is nearly: