In $a$ smooth stationary cart of length $d, a$ small block is projected along it's length with velocity $v$ towards front. Coefficient of restitution for each collision is $e$. The cart rests on $a$ smooth ground and can move freely. The time taken by block to come to rest $w.r.t$. cart is 

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 ............... $^o$

Which one of the following statements does not hold good when two balls of masses $m _1$ and $m _2$ undergo elastic collision

A body starts falling freely from height $\mathrm{H}$ hits an inclined plane in its path at height $\mathrm{h}$. As a result of this perfectly elastic impact, the direction of the velocity of the body becomes horizontal. The value of $\frac{\mathrm{H}}{\mathrm{h}}$ for which the body will take the maximum time to reach the ground is______.

Two identical balls $A$ and $B$ having velocities of $0.5\, m s^{-1}$ and $-0.3 \, m s^{-1}$ respectively collide elastically in one dimension. The velocities of $B$ and $A$ after the collision respectively will be

In the figure shown, a small ball hits obliquely a smooth and horizontal surface with speed $u$ whose $x$ and $y$ components are indicated. If the coefficient of restitution is $\frac{1}{2}$, then its $x$ and $y$ components $v_x$ and $v_y$ just after collision are respectively