When a $4\, kg$ mass is hung vertically on a light spring that obeys Hooke's law, the spring stretches by $2\, cms$. The work required to be done by an external agent in stretching this spring by $5\, cms$ will be ……… $joule$       $(g = 9.8\,metres/se{c^2})$

When a force is applied on a wire of uniform cross-sectional area $3 \times {10^{ – 6}}\,{m^2}$ and length $4m$, the increase in length is $1\, mm.$ Energy stored in it will be $(Y = 2 \times {10^{11}}\,N/{m^2})$

One end of a slack wire (Young's modulus $Y$, length $L$ and cross-sectional area $A$ ) is clamped to a rigid wall and the other end to a block (mass $m$ ), which rests on a smooth horizontal plane. The block is set in motion with a speed $v$. What is the maximum distance, then the block will travel after the wire becomes taut?

Given : $\sigma$ is the compressibility of water, $\rho$ is the density of water and $K$ is the  bulk modulus of water. What is the energy density of water at the bottom of a lake $‘h’$  metre deep ?

A $2 \,m$ long rod of radius $1 \,cm$ which is fixed from one end is given a twist of $0.8$ radians. The shear strain developed will be