A particle of mass $m$ with an initial velocity $u\hat i$ collides perfectly elastically with a mass $3m$ at rest. It moves with a velocity $v\hat j$ after collision, then, $v$ is given by
$v=\sqrt{\frac{2}{3}} u$
$v =\frac{1}{\sqrt{6}} u$
$v=\frac{u}{\sqrt{3}}$
$v=\frac{u}{\sqrt{2}}$
Two identical ball bearings in contact with each other and resting on a frictionless table are hit head-on by another ball bearing of the same mass moving initially with a speed $V$. If the collision is elastic, which of the following figure is a possible result after collision ?
A bob of mass $m$, suspended by a string of length $I_1$, is given a minimum velocity required to complete a full circle in the vertical plane, At the highest point, it collides elastically with another bob of mass $m$ suspended by a string of length $I_2$, which is initially at rest. Both the strings are mass-less and inextensible. If the second bob, after collision acquires the minimum speed required to complete a full circle in the vertical plane, the ratio $\frac{I_1}{I_2}$ is :
In the above question, if another body is at rest, then velocity of the compound body after collision is
Three objects $A, B$ and $C$ are kept in a straight line on a frictionless horizontal surface. The masses of ${A}, {B}$ and ${C}$ are ${m}, 2\, {m}$ and $2\, {m}$ respectively. $A$ moves towards ${B}$ with a speed of $9$ ${m} / {s}$ and makes an elastic collision with it. Thereafter $B$ makes a completely inelastic collision with $C.$ All motions occur along same straight line. The final speed of $C$ is $....\,{m} / {s}$
A moving block having mass $m,$ collides with another stationary block having mass $4\,m$ . The lighter block comes to rest after collision. When the initial velocity of the lighter block is $v,$ then the value of coefficient of restitution $( e)$ will be