$A$ large ball of mass $M$,moving with velocity $u$,strikes a small ball of mass $m$,which is at rest. After the collision,the small ball attains velocity $u$ and the large ball attains velocity $v$. What is the value of $v$?

Two identical balls $A$ and $B$ of equal mass $m$ are lying on a smooth surface as shown in the figure. If ball $A$ hits ball $B$ at rest with a velocity $16 \,ms^{-1}$,then the coefficient of restitution $e$ between $A$ and $B$ so that $B$ just reaches the highest point of the smooth inclined plane of height $5 \,m$ is $\left(g=10 \,ms^{-2}\right)$

$A$ ball impinges directly on a similar ball of same mass at rest. If $1/4$ of the kinetic energy is lost by the impact,the value of the coefficient of restitution is

$A$ ball of mass $m$ is moving with a speed $V$ as shown in the figure. It undergoes an inelastic collision with a ball of mass $2m$ which was initially at rest. The velocity of the ball of mass $2m$ after the collision is given by

$A$ body of mass $m_1$ moving with a velocity $3 \, ms^{-1}$ collides with another body at rest of mass $m_2$. After the collision,the velocities of the two bodies are $2 \, ms^{-1}$ and $5 \, ms^{-1}$ respectively along the direction of motion of $m_1$. The ratio $\frac{m_1}{m_2}$ is:

$A$ ball with a speed of $9\, m/s$ collides with another identical ball at rest. After the collision,the direction of each ball makes an angle of $30^{\circ}$ with the original direction. The ratio of velocities of the balls after collision is $x : y$ where $x$ is........