The graph between the resistive force $ F$ acting on a body and the distance covered by the body is shown in the figure. The mass of the body is $25\, kg$ and initial velocity is $2\, m/s$. When the distance covered by the body is $4m$, its kinetic energy would be .............. $\mathrm{J}$

Two monkeys with the same mass stand on a branch at height $h$ above the horizontal jungle floor. Monkey $A$ steps off the branch holding the end of an inextensible rope of length $L$ whose other end is tied to another branch at height $H$, lets go at the bottom of the swing, and falls freely to the floor, as shown below. Monkey $B$ steps off and falls straight downward. Then, neglecting air resistance but not the tension in the rope, the total work $W$ done on each monkey and the speed $v$ with which each hits the floor are as follows:

A uniform chain (mass $M,$ length $L$) is released from rest from a smooth horizontal surface as shown in the figure. Velocity of the chain at the instant it completely comes out of the table will be

A rocket accelerates straight up by ejecting gas downwards. In a small time interval $\Delta t$, it ejects a gas of mass $\Delta m$ at a relative speed $u$. Calculate $KE$ of the entire system at $t + \Delta t$ and $t$ and show that the device that ejects gas does work $=(\frac {1}{2})\Delta mu^2$ in this time interval (negative gravity).

A ball is dropped from a height of $20\, cm$. Ball rebounds to a height of $10\, cm$. What is the loss of energy ? ................ $\%$

A body of $\mathrm{m} \mathrm{kg}$ slides from rest along the curve of vertical circle from point $A$ to $B$ in friction less path. The velocity of the body at $B$ is:

(given, $\mathrm{R}=14 \mathrm{~m}, \mathrm{~g}=10 \mathrm{~m} / \mathrm{s}^2$ and $\sqrt{2}=1.4$ )