A particle of mass $500 \mathrm{g}$ is moving in a straight line with velocity $v=\mathrm{b}{x}^{\frac{5}{2}}$. The work done by the net force during its displacement from $x=0$ to $x=4 \mathrm{m}$ is  (Take $\mathrm{b}=0.25 { \mathrm{m}}^{\frac{-3}{2}}{\mathrm{s}}^{-1}$).

In the given figure, the block of mass $m$ is dropped from the point $A$. The expression for kinetic energy of block when it reaches point $B$ is

As per the given figure, two blocks each of mass $250 \mathrm{g}$ are connected to a spring of spring constant $2 \mathrm{N} {\mathrm{m}}^{-1}$. If both are given velocity $v$ in opposite directions, then maximum elongation of the spring is

A block of mass '$m$' (as shown in figure) moving with kinetic energy $E$ compresses a spring through a distance $25 \mathrm{cm}$ when, its speed is halved. The value of spring constant of used spring will be $nE \mathrm{N} {\mathrm{m}}^{-1}$ for $n=$_____.