$A$ billiard ball of mass $M$,moving with velocity $v_1$ collides with another ball of the same mass but at rest. If the collision is elastic,the angle of divergence after the collision is (in $^{\circ}$)

$A$ body $A$ of mass $m=0.1 \; kg$ has an initial velocity of $3 \hat{i} \; ms^{-1}$. It collides elastically with another body $B$ of the same mass which has an initial velocity of $5 \hat{j} \; ms^{-1}$. After the collision,$A$ moves with a velocity $\vec{v}_A = 4(\hat{i} + \hat{j}) \; ms^{-1}$. The energy of $B$ after the collision is written as $\frac{x}{10} \; J$. The value of $x$ is:

Two small particles of equal masses start moving in opposite directions from a point $A$ in a horizontal circular orbit. Their tangential velocities are $v$ and $2v$,respectively,as shown in the figure. Between collisions,the particles move with constant speeds. After making how many elastic collisions,other than that at $A$,will these two particles again reach the point $A$?

$A$ ball moving with velocity $V$ undergoes a perfectly elastic collision with an identical ball moving in the opposite direction with velocity $2V$. Taking the direction of $V$ as positive,find the velocities of both balls after the collision.

Two balls of mass $5 \ kg$ are moving in opposite directions with the same speed of $5 \ m/s$. They undergo a head-on elastic collision. Find the final velocity of the balls in $m/s$.

$A$ moving particle collides with a stationary particle of mass $\frac{1}{n}$ times the mass of the moving particle. The fraction of its kinetic energy transferred to the stationary particle is: