A ball impinges directly on a similar ball at rest. If $1/4^{th}$ of the kinetic energy is lost by the impact, the value of coefficient of restitution is
$\frac {1}{2\sqrt 2}$
$\frac {1}{\sqrt 3}$
$\frac {1}{\sqrt 2}$
$\frac {\sqrt 3}{2}$
A sphere strikes a wall and rebounds with coefficient of restitution $1/3$. If it rebounds with a velocity of $0.1\, m/sec$ at an angle of $60^o$ to the normal to the wall, the loss of kinetic energy is
Three particles each of mass $m$ are located at the vertices of an equilateral triangle $ABC$. They start moving with equal speeds $v$ each along the medians of the triangle and collide at its centroid $G$. If after collision, $A$ comes to rest and $B$ retraces its path along $GB,$ then $C$
Two particles of equal mass $\mathrm{m}$ have respective initial velocities $u\hat{i}$ and $u\left(\frac{\hat{\mathrm{i}}+ \hat{\mathrm{j}}}{2}\right) .$ They collide completely inelastically. The energy lost in the process is
Explain the total linear momentum is conserved in an elastic collision and also explain the inelastic collision and completely elastic collision.
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