An object of mass $M$ is much heavier than another object of mass $m$. The heavy object moving with speed $v$ undergoes an elastic collision with the light object at rest. What will be the speed of the light object after the collision?

In a scattering experiment,a particle of mass $2m$ collides with another particle of mass $m$,which is initially at rest. Assuming the collision to be perfectly elastic,the maximum angular deviation $\theta$ of the heavier particle,as shown in the figure,in radians is:

The bob $A$ of a pendulum,released from a horizontal position to the vertical,hits another bob $B$ of the same mass at rest on a table as shown in the figure. If the length of the pendulum is $1\,m$,calculate:
$(a)$ The height to which bob $A$ will rise after the collision.
$(b)$ The speed with which bob $B$ starts moving.
Neglect the size of the bobs and assume the collision to be elastic.

$A$ 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:

An alpha-particle of mass $m$ undergoes a $1$-dimensional elastic collision with a nucleus of unknown mass $M$ at rest. It is scattered directly backwards,losing $64\%$ of its initial kinetic energy. The mass of the nucleus is .......... $m$.

$A$ ball of mass $m$ is thrown at a wall with speed $v$ at an angle $\theta$ with the normal to the wall. If the coefficient of restitution is $e$,what will be the magnitude and direction of the velocity of the ball after the collision with respect to the wall?