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

Two billiard balls undergo a head-on collision. Ball $1$ is twice as heavy as ball $2$. Initially, ball $1$ moves with a speed $v$ towards ball $2$ which is at rest. Immediately after the collision, ball $1$ travels at $a$ speed of $v/3$ in the same direction. What type of collision has occured?

Two balls in free space are colliding with each other. Which of the following statement regarding linear momentum conservation of the system is true ?

A mass $m_1$ moves with a great velocity. It strikes another mass $m _2$ at rest in a head on collision. It comes back along its path with low speed, after collision. Then

$A$ 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

Two massless string of length $5\, m$ hang from the ceiling very near to each other as shown in the figure. Two balls $A$ and $B$ of masses $0.25 \,kg$ and $0.5 \,kg$ are attached to the string. The ball $A$ is released from rest at $a$ height $0.45\, m$ as shown in the figure. The collision between two balls is completely elastic. Immediately after the collision, the kinetic energy of ball $B$ is $1\, J$. The velocity of ball $A$ just after the collision is