Particle $A$ makes a perfectly elastic collision with another particle $B$ at rest. They fly apart in opposite direction with equal speeds. If their masses are $m_A$ and $m_B$ respectively, then

A ball is thrown horizontally from a height with a certain initial velocity at time $t=0$. The ball bounces repeatedly from the ground with the coefficient of restitution less than $1$ as shown below. Neglecting air resistance and taking the upward direction as positive, which figure qualitatively depicts the vertical component of the ball's velocity $v_y$ as a function of time $t$ ?

Three objects $A$, $B$ and $C$ are kept in a straight line on a frictionless horizontal surface. These have masses $m, 2 m$ and $m$, respectively. The object $A$ moves towards $B$ with a speed $9 \mathrm{~m} / \mathrm{s}$ and makes an elastic collision with it. Thereafter, $B$ makes completely inelastic collision with $C$. All motions occur on the same straight line. Find the final speed (in $\mathrm{m} / \mathrm{s}$ ) of the object $\mathrm{C}$.

Two identical balls $A$ and $B$ are released from the positions shown in figure. They collide elastically on horizontal portion $MN$ . The ratio of the heights attained by $A$ and $B$ after collision will be : (neglect friction)

A neutron makes a head-on elastic collision with a stationary deuteron. The fractional energy loss of the neutron in the collision is

A point mass $M$ moving with a certain velocity collides with a stationary point mass $M / 2$. The collision is elastic and in one-dimension. Let the ratio of the final velocities of $M$ and $M / 2$ be $x$. The value of $x$ is