$A$ steel ball of radius $2 \,cm$ is at rest on a frictionless surface. Another steel ball of radius $4 \,cm$ moving with velocity of $81 \,cm \,s^{-1}$ collides elastically with the ball which is at rest. After collision, the ball with radius of $2 \,cm$ moves with a speed of:

$A$ particle of mass $m$ moving with kinetic energy $E$ collides head-on elastically with another particle of mass $2m$ at rest. After the collision,the kinetic energy of the first particle is:

$A$ particle $P$ moving with speed $v$ undergoes a head-on elastic collision with another particle $Q$ of identical mass but at rest. After the collision:

Which of the following potential energy curves in the figure cannot possibly describe the elastic collision of two billiard balls? Here $r$ is the distance between the centres of the balls.

Two masses $m_A$ and $m_B$ moving with velocities $v_A$ and $v_B$ in opposite directions collide elastically. After the collision,the masses $m_A$ and $m_B$ move with velocities $v_B$ and $v_A$ respectively. The ratio $\frac{m_A}{m_B} = $

Consider the collision depicted in the figure to be between two billiard balls with equal masses $m_{1} = m_{2}$. The first ball is called the cue, while the second ball is called the target. The billiard player wants to 'sink' the target ball in a corner pocket, which is at an angle $\theta_{2} = 37^{\circ}$. Assume that the collision is elastic and that friction and rotational motion are not important. Obtain $\theta_{1}$.