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

The elastic potential energy stored in a steel wire of length $20\,m$ stretched through $2 \,m$ is $80\,J$. The cross sectional area of the wire is $.........\,mm ^2$ (Given, $y =2.0 \times 10^{11}\,Nm ^{-2}$ )

A wire fixed at the upper end stretches by length $l$ by applying a force $F$. The work done in stretching is

A wire suspended vertically from one of its ends is stretched by attaching a weight of $200\, N$ to the lower end. The weight stretches the wire by $1\, mm$ Then the elastic energy stored in the wire is ........ $J$

The work done per unit volume to stretch the length of area of cross-section $2 \,mm ^2$ by $2 \%$ will be ....... $MJ / m ^3$ $\left[Y=8 \times 10^{10} \,N / m ^2\right]$

If the potential energy of a spring is $V$ on stretching it by $2\, cm$, then its potential energy when it is stretched by $10 \,cm$ will be