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

Given below are two statements. One is labelled as Assertion $(A)$ and the other is labelled as Reason $(R)$. Three identical spheres of same mass undergo one-dimensional motion as shown in the figure with initial velocities $v_{A} = 5 \ m/s$,$v_{B} = 2 \ m/s$,$v_{C} = 4 \ m/s$. If we wait sufficiently long for elastic collisions to happen,then $v_{A} = 4 \ m/s$,$v_{B} = 2 \ m/s$,$v_{C} = 5 \ m/s$ will be the final velocities.
Reason $(R)$: In an elastic collision between identical masses,two objects exchange their velocities. In the light of the above statements,choose the correct answer from the options given below:

$A$ smooth sphere $A$ of mass $m$ collides elastically with an identical sphere $B$ at rest. The velocity of $A$ before collision is $8 \ m/s$ in a direction making $60^{\circ}$ with the line of centers at the time of impact.
$(i)$ The sphere $A$ comes to rest after collision.
$(ii)$ The sphere $B$ will move with a speed of $8 \ m/s$ after collision.
$(iii)$ The directions of motion of $A$ and $B$ after collision are at right angles.
$(iv)$ The speed of $B$ after collision is $4 \ m/s$.
The correct option is:

What happens when two identical bodies moving in opposite directions undergo a perfectly elastic collision?

$A$ body of mass $m$ moving with velocity $v$ makes a head-on collision with another body of mass $2m$ which is initially at rest. What is the ratio of the kinetic energy of the colliding body before and after the collision (in $: 1$)?

$A$ particle of mass $m_1$ collides with a particle of mass $m_2$ at rest. After the elastic collision,the two particles move at an angle of $90^{\circ}$ with respect to each other. The ratio $\frac{m_2}{m_1}$ is