$A$ sphere of mass $m$ travelling at constant speed $v$ strikes another sphere of the same mass. If the coefficient of restitution is $e$,then the ratio of the velocities of both spheres just after the collision is:

Two solid rubber balls $A$ and $B$ have masses $200 \ g$ and $400 \ g$ respectively. They are moving towards each other,with ball $A$ having a velocity of $0.3 \ m/s$. After the collision,both balls come to rest. What is the velocity of ball $B$ in $m/s$?

$A$ block of mass '$m$' with an initial kinetic energy '$E$' moves up an inclined plane of inclination '$\theta$'. If '$\mu$' is the coefficient of friction between the plane and the body, the work done against friction before coming to rest is

$A$ mass $m$ moving horizontally with velocity $v_0$ strikes a pendulum of mass $m$. If the two masses stick together after the collision,then the maximum height reached by the pendulum is

In two separate collisions,the coefficients of restitution $e_1$ and $e_2$ are in the ratio $3:1$. In the first collision,the relative velocity of approach is twice the relative velocity of separation. Find the ratio between the relative velocity of approach and the relative velocity of separation in the second collision.

$A$ wooden block of mass $M$ rests on a horizontal surface. $A$ bullet of mass $m$ moving in the horizontal direction strikes and gets embedded in it. The combined system covers a distance $x$ on the surface. If the coefficient of friction between the wood and the surface is $\mu$,the speed of the bullet at the time of striking the block is: