A particle of mass $m$ moving with a speed $v$ hits elastically another stationary particle of mass $2\ m$ in a fixed smooth horizontal circular tube of radius $R$. Find the time when the next collision will take place?

- A
$\frac{{\pi R}}{v}$

- B
$\frac{{2\pi R}}{v}$

- C
$\frac{{4\pi R}}{v}$

- D
$\frac{{6\pi R}}{v}$

Hail storms are observed to strike the surface of the frozen lake at $30^o$ with the vertical and rebound at $60^o$ with the vertical. Assume contact to be smooth, the coefficient of restitution is

- [AIIMS 2017]

A body of mass $4\ kg$ collides head-on elastically with another body of mass $2\ kg$ kept at rest in free space. Time of collision is $0.02\ sec$ and average impulse force acted on each bodies is $100\ N$. Find the velocity of the $2\ kg$ body after the impact

A sphere collides with another sphere of identical mass. After collision, the two spheres move. The collision is inelastic. Then the angle between the directions of the two spheres is

This question has statement $1$ and statement $2$ . Of the four choices given after the statements, choose the one that best describes the two statements.

Statement $- 1$: A point particle of mass m moving with speed $u$ collides with stationary point particle of mass $M$. If the maximum energy loss possible is given as $f$ $\left( {\frac{1}{2}m{v^2}} \right)$ then $ f = \left( {\frac{m}{{M + m}}} \right)$

Statement $-2$: Maximum energy loss occurs when the particles get stuck together as a result of the collision.

- [JEE MAIN 2013]

A body of mass $1\,kg$ collides head on elastically with a stationary body of mass $3\,kg$. After 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 collision is $..........ms ^{-1}$

- [JEE MAIN 2023]