$A$ sphere of mass $10 \ kg$ moving with a velocity of $10 \ m/s$ undergoes an elastic collision with a body of mass $5 \ kg$ moving in the same direction with a velocity of $4 \ m/s$. What are their velocities after the collision?

Consider an elastic collision of a particle of mass $m$ moving with a velocity $u$ with another particle of the same mass at rest. After the collision, the projectile and the struck particle move in directions making angles $\theta_1$ and $\theta_2$ respectively with the initial direction of motion. The sum of the angles, $\theta_1 + \theta_2$, is equal to: (in $^\circ$)

$A$ 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 the collision. Then:

$A$ body of mass $m$ moving with a velocity $v$ collides head-on with another body of mass $2m$ at rest. If the coefficient of restitution between the two bodies is $e$,then the ratio of the velocities of the two bodies after collision is:

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

In an elastic collision of two billiard balls,which of the following quantities remain conserved during the short time of collision of the balls? (i.e.,when they are in contact)
$(a)$ Kinetic energy.
$(b)$ Total linear momentum.
Give reason for your answer in each case.