A ball strikes a horizontal surface as shown in figure. If co-efficient of restitution $e = 1/ \sqrt 3$,  then angle $\theta$ is  ............... $^o$

An object of mass $m _{1}$ collides with another object of mass $m _{2}$, which is at rest. After the collision the objects move with equal speeds in opposite direction. The ratio of the masses $m _{2}: m _{1}$ is

A particle of mass $m$ is moving along the $x$ -axis with initial velocity $u \hat i$. It collides elastically with a particle of mass $10\, m$ at rest and then moves with half its initial kinetic energy (see figure). If $\sin \theta_{1}=\sqrt{n} \sin \theta_{2}$ then value of $n$ is.....

An object is dropped from a height $h$ from the ground. Every time it hits the ground it looses $50\%$ of its kinetic energy. The total distance covered as $t \to \infty $ 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 .............. $^o$

A ball of mass $m$ strikes the inclined face of the wedge normally with speed $v_0$. The wedge is at rest on a rough horizontal surface before collision. The conservation of momentum is applicable for the event of collision for

$(i)$ $m$ as system, along $Y'$
$(ii) $ $M$ as system, along $Y'$
$(iii)$ $(M + m)$ as system, along $X$
$(iv)$  $(M + m)$ as system, along $Y$
Which of the following is correct?