A body of mass ${M}$ moving at speed ${V}_{0}$ collides elastically with a mass $'m'$ at rest. After the collision, the two masses move at angles $\theta_{1}$ and $\theta_{2}$ with respect to the initial direction of motion of the body of mass ${M}$. The largest possible value of the ratio ${M} / {m}$, for which the angles $\theta_{1}$ and $\theta_{2}$ will be equal, is :

Blocks of masses $m , 2 m , 4 m$ and $8 m$ are arranged in a line on a frictionless floor. Another block of mass $m ,$ moving with speed $v$ along the same line (see figure) ollides with mass $m$ in perfectly inelastic manner. All the subsequent collisions are also perfectly inelastic. By the time the last block of mass $8 m$ starts moving the total energy loss is $p \%$ of the original energy. Value of $'p'$ is close to

A body of mass $m$  moving with velocity $v$ collides head on with another body of mass $2m $ which is initially at rest. The ratio of K.E. of colliding body before and after collision will be

Two solid rubber balls $A$ and $B$ having masses $200$ and $400\, gm$ respectively are moving in opposite directions with velocity of $A$ equal to $0.3 \,m/s$. After collision the two balls come to rest, then the velocity of $B$ is .............. $\mathrm{m} / \mathrm{s} $

The bob $A$ of a simple pendulum is released when the string makes an angle of ${45^o}$with the vertical. It hits another bob $B$ of the same material and same mass kept at rest on the table. If the collision is elastic

Three different projectiles, each with the same mass, are fired with speed $v$ at a wall. In case $A,$ the projectile bounces straight back with speed $v.$ In case $B$, the projectile sticks to the wall. In case $C$, the projectile crashes through the wall and emerges with half its original speed. These three cases are shown here.

Place the impulse exerted by the wall on the projectile in each of these three cases in the correct order.