Two spheres $A$ and $B$ of masses $m_1$ and $m_2$ respectively collide. Sphere $A$ is at rest initially and sphere $B$ is moving with velocity $v$ along the $x$-axis. After the collision,sphere $B$ has a velocity of $\frac{v}{2}$ in a direction perpendicular to the original direction. The mass $A$ moves after the collision in the direction:

$A$ 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:

If a shell fired from a cannon explodes in mid-air,then which of the following is true?

$A$ particle of mass $m$ is initially at rest at the origin. It is subjected to a force and starts moving along the $x$-axis. Its kinetic energy $K$ changes with time as $dK/dt = \gamma t$,where $\gamma$ is a positive constant of appropriate dimensions. Which of the following statements is (are) true?
$(A)$ The force applied on the particle is constant
$(B)$ The speed of the particle is proportional to time
$(C)$ The distance of the particle from the origin increases linearly with time
$(D)$ The force is conservative

$A$ body of mass $100 \ gm$ moves with a constant speed along a circular path of radius $r$. What is the work done during one complete revolution?

Block $A$ of mass $m$ is hanging from a vertical spring of spring constant $k$ and is at rest. Block $B$ of mass $m$ strikes block $A$ with velocity $v$ and sticks to it. The velocity $v$ for which the spring just attains its natural length is: