A sphere $P$ of mass $m$ and moving with velocity $v$ undergoes an oblique and  perfectly elastic collision with an identical sphere $Q$ initially at rest. The angle $\theta$ between the velocities of the spheres after the collision shall be .............. $^o$

Body $A$ of mass $4 \;\mathrm{m}$ moung with speed $u$ collides with another body $B$ of mass $2\; \mathrm{m}$, at rest. The collision is head on and elastic in nature. After the collision the fraction of energy lost by the colliding body $A$ is

A ball falling freely from a height of $4.9\,m,$ hits a horizontal surface. If $e = \frac {3}{4}$ , then the ball will hit the surface, second time after .............. $\mathrm{s}$

Two pendulums with identical bobs and lengths are suspended from a common support such that in rest position the two bobs are in contact (figure). One of the bobs is released after being displaced by $10^o$ so that it collides elastically head-on with the other bob.

$(a)$ Describe the motion of two bobs.

$(b)$ Draw a graph showing variation in energy of either pendulum with time, for $0\, \leqslant \,t\, \leqslant \,2T$, where $T$ is the period of each pendulum.

$A$ ball is of mass $m$, strikes a smooth ground at angle $\alpha$ as shown in figure and is deflected at angle $\beta$. The coefficient of restitution will be

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