Two balls having mass $2 \mathrm{kg}$ and $3 \mathrm{kg}$ are approaching each other with velocities $3 \mathrm{m} {\mathrm{s}}^{-1}$ and $2 \mathrm{m} {\mathrm{s}}^{-1}$ respectively on the horizontal frictionless surface. They undergo a head-on elastic collision. Find out the maximum potential energy of deformation.

A string of negligible mass going over a clamped pulley of mass $\mathrm{m}$ supports a block of mass $M$ as shown in the figure. The force on the pulley by the clamp is given by

A small block slides with velocity $0.5\sqrt{gr}$ on the horizontal frictionless surface as shown in the Figure. The block leaves the surface at point $C$. The angle $\theta$ in the Figure is :

A particle is moving in the vertical plane. It is attached at one end of a string of length I whose other end is fixed. The velocity at the lowest point is $u$. The tension in the string $\overrightarrow{T}$ is and acceleration of the particle $\overrightarrow{a}$ is at any position. Then, $\overrightarrow{T}.\overrightarrow{a}$ is zero at the highest point.

In the above question, $\overrightarrow{T}.\overrightarrow{a}$ is non-negative at the lowest point for 

A particle is moving in a circular path on the vertical plane. It is attached at one end of a string of length I whose other end is fixed. The velocity of the particle at the lowest point is $u$. The tension in the string is $\overrightarrow{T}$ and the acceleration of the particle is $\overrightarrow{a}$ at any position. Then, $\overrightarrow{T}.\overrightarrow{a}$ is zero at the highest point if

A bob of mass $M$ is suspended by a massless string of length $L$. The horizontal velocity $V$ at position $A$ is just sufficient to make it reach the point $B$. The angle $\theta$ at which the speed of the bob is half of that at $A$, satisfies