$A$ sphere of mass $m$,moving with velocity $3u$,collides head-on with another identical sphere at rest. If $e$ is the coefficient of restitution,what will be the ratio of the velocity of the second sphere to that of the first sphere after the collision?

$A$ block of mass $m$ moving on a frictionless surface at speed $v$ collides elastically with a block of the same mass,initially at rest. Now,the first block moves at an angle $\theta$ with its initial direction and has speed $v_1$. The speed of the second block after the collision is

Two masses $m_1$ and $m_2$ moving with velocities $v_1$ and $v_2$ in opposite directions collide elastically and after collision masses $m_1$ and $m_2$ move with velocity $v_2$ and $v_1$ respectively. The ratio $\left(\frac{m_2}{m_1}\right)$ is

$A$ moving body with a mass $m_1$ and velocity $u$ strikes a stationary body of mass $m_2$. The masses $m_1$ and $m_2$ should be in the ratio $\frac{m_1}{m_2}$,so as to decrease the velocity of the first body to $\frac{2u}{3}$ and give a velocity of $v$ to $m_2$,assuming a perfectly elastic impact. Then,the ratio $\frac{m_1}{m_2}$ is

$A$ $2\, kg$ block moving with $10\, m/s$ strikes a spring of constant $\pi^2\, N/m$ attached to a $2\, kg$ block at rest kept on a smooth floor. The velocity of the rear $2\, kg$ block after it separates from the spring will be ..... $m/s$.

In an elastic collision of two billiard balls,which of the following quantities remain conserved during the short time of collision of the balls? (i.e.,when they are in contact)
$(a)$ Kinetic energy.
$(b)$ Total linear momentum.
Give reason for your answer in each case.