Ball $A$ of mass $50 \ gm$ and speed $10 \ m/s$ collides with another ball $B$ of mass $10 \ gm$ and speed $15 \ m/s$ travelling in opposite directions. Determine the final speed of ball $B$,if the coefficient of restitution is $\frac{2}{5}$.

$A$ ball is dropped from a height of $20 \ m$. If it loses $20\%$ of its energy upon collision with the ground,what is the coefficient of restitution?

$A$ smooth sphere moves on a horizontal surface with a velocity vector $2\hat{i} + 2\hat{j}$ before it strikes a vertical wall. The wall is parallel to the $\hat{j}$ vector,and the coefficient of restitution between the sphere and the wall is $e = 1/2$. What will be the velocity vector of the sphere after it strikes the wall?

$A$ ball makes a head-on collision with another ball of twice its mass,which is initially at rest,with a velocity of $1.5 \ m/s$. If the coefficient of restitution is $0.6$,what will be their velocities after the collision?

$A$ bullet of mass $m$ and speed $v$ hits a pendulum bob of mass $M$ at time $t_1$,and passes completely through the bob. The bullet emerges at time $t_2$ with a speed of $v/2$. The pendulum bob is suspended by a stiff rod of length $l$ and negligible mass. After the collision,the bob can barely swing through a complete vertical circle. At time $t_3$,the bob reaches the highest position. What quantities are conserved in this process?

$A$ moving block having mass $m$ collides with another stationary block having mass $4m$. The lighter block comes to rest after the collision. If the initial velocity of the lighter block is $v$,then the value of the coefficient of restitution $(e)$ will be: