In one dimensional case, the relationship between force and position is shown in the figure. The work done by the force in displacing a body from $x = 1\, cm$ to $x = 5\, cm$ is ............ $\mathrm{ergs}$

In the figure shown the potential energy $(U)$ of a particle is plotted against its position $'x'$ from origin. The particle at

$A$ ball is dropped from height $5m$. The time after which ball stops rebounding if coefficient of restitution between ball and ground $e = 1/2$, is .................. $\mathrm{sec}$

A sphere is suspended by a thread of length $\ell $. What minimum horizontal velocity has to be imparted to the sphere for it to reach the height of the suspension

$ABCDE$ is a channel in the vertical plane, part $BCDE$ being circular with radius $r$ . A block is released from $A$ and slides without friction and without rolling. The block will complete the loop if $h$ is

A long spring, when stretched by a distance $x,$ has the potential energy $u.$ On increasing the stretching to $nx.$ The potential energy of the spring will be