A point mass of $1 \mathrm{~kg}$ collides elastically with a stationary point mass of $5 \mathrm{~kg}$. After their collision, the $1 \mathrm{~kg}$ mass reverses its direction and moves with a speed of $2 \mathrm{~ms}^{-1}$. Which of the following statement(s) is (are) correct for the system of these two masses?

$(A)$ Total momentum of the system is $3 \mathrm{~kg} \mathrm{~ms}^{-1}$

$(B)$ Momentum of $5 \mathrm{~kg}$ mass after collision is $4 \mathrm{~kg} \mathrm{~ms}^{-1}$

$(C)$ Kinetic energy of the centre of mass is $0.75 \mathrm{~J}$

$(D)$ Total kinetic energy of the system is $4 \mathrm{~J}$

Explain oblique collision.

A simple pendulum, made of a string of length $l$ and a bob of mass $m$ , is released from a small angle $\theta_0$. It strikes a block of mass $M$, kept on a horizontal surface at its lowest point of oscillations, elastically. It bounces back and goes up to an angle $\theta_1$. Then $M$ is given by

On a frictionless surface, a block of mass $M$ moving at speed $V$ collides elastically with another block of same mass $M$ which is initially at rest. After collision the first block moves at an angle $\theta$ to its initial direction and has a speed $\frac{V}{3}$ The second block's speed after the collision is

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A ball is dropped from height $5\,\,m$. The time after which ball stops rebounding if coefficient of restitution between ball and ground $e = 1/2$, is ............. $\mathrm{sec}$