An object of mass $m$ is sliding down a hill of arbitrary shape and after traveling a certain horizontal path stops because of friction. The friction coefficient is different for different segments of the entire path but it is independent of the velocity and direction of motion. The work done that a force must perform to return the object  its initial position along the same path would be :-

Consider the collision depicted in Figure to be between two billiard balls with equal masses $m_{1}=m_{2}$ The first ball is called the cue while the second ball is called the target. The billiard player wants to 'sink' the target ball in a corner pocket, which is at an angle $\theta_{2}=37^{\circ} .$ Assume that the collision is elastic and that friction and rotational motion are not important. Obtain $\theta_{1}$

A ball is released from a height of $10\, m$. If after the impact there is loss of $40\%$ in its  energy, the ball shall rise upto- ................. $\mathrm{m}$

A particle is moving in a circular path of radius a under the action of an attractive potential $U = - \frac{k}{{2{r^2}}}$ Its total energy is

A porter lifts a heavy suitcase of mass $80\, {kg}$ and at the destination lowers it down by a distance of $80\, {cm}$ with a constant velocity. Calculate the workdone by the porter in lowering the suitcase. (take $g=9.8\, {ms}^{-2}$ ) (In ${J}$)

A body of mass $0.5\; kg$ travels in a stratght line with velocity $v=a x^{3 / 2}$ where $a=5\; m ^{-1 / 2} s ^{-1}$ What is the work done (in $J$) by the net force during its displacement from $x=0$ to $x=2\; m ?$