$A$ sphere of mass $M$ moving with velocity $u$ undergoes a perfectly elastic collision with a stationary sphere of mass $m$. If their velocities after the collision are $V$ and $v$ respectively,what is the value of $v$?

$A$ 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

In an elastic collision of two particles,which of the following quantities is conserved?

$A$ body of mass $1\,kg$ collides head-on elastically with a stationary body of mass $3\,kg$. After the collision,the smaller body reverses its direction of motion and moves with a speed of $2\,m/s$. The initial speed of the smaller body before the collision is $..........\,m/s$.

$A$ smooth sphere of mass $M$ moving with velocity $u$ directly collides elastically with another sphere of mass $m$ at rest. After collision,their final velocities are $V$ and $v$ respectively. The value of $v$ is

$A$ ball is dropped from a height of $80 \ m$ on a surface which is at rest. Find the height attained by the ball after the $2^{nd}$ collision if the coefficient of restitution is $e = 0.5$.