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

$A$ particle of mass $1\, kg$ moving with velocity $1\, m/s$,collides elastically with another particle of mass $m$ initially at rest. In the collision,the particle of mass $1\, kg$ loses $\frac{3}{4}$ of its kinetic energy $(K.E.)$. The value of $m$ is:

Assertion $(A)$: In an elastic collision between two bodies,the relative speed of the bodies after collision is equal to the relative speed before the collision.
Reason $(R)$: In an elastic collision,the linear momentum of the system is conserved.

Six identical balls are lined up in a straight groove on a horizontal frictionless surface. Two similar balls,each moving with a velocity $v$,collide elastically with the row of $6$ balls from the left. What will happen?

$A$ smooth sphere $A$ is moving on a frictionless horizontal plane with angular speed $\omega$ and center of mass with velocity $v$. It collides elastically and head-on with an identical sphere $B$ at rest. Neglect friction everywhere. After the collision,their angular speeds are $\omega_A$ and $\omega_B$ respectively. Then

Two billiard balls of mass $0.05\,kg$ each,moving in opposite directions with $10\,m/s$,collide and rebound with the same speed. If the time duration of contact is $t = 0.005\,s$,then the force exerted on the balls due to each other is $\dots N$.