If the pressure on a body is increased from 200 kPa to 250 kPa , the volume of the body decreases by $0.25 \%$. The compressibility of the material of the body is (in $\mathrm{m}^2 \mathrm{~N}^{-1}$ )

When a wire made of material with Young's modulus $\gamma$ is subjected to a stress $S$, the elastic potential energy per unit volume stored in the wire is

The force required to stretch a steel wire of area of cross-section $1 \mathrm{~mm}^2$ to double its length is

(Young's modulus of steel $=2 \times 10^{11} \mathrm{~N}-\mathrm{m}^{-2}$ )

When a wire of length ' $L$ ' clamped at one end is pulled by a force ' $F$ ' from the other end, its length increases by ' $L$ '. If the radius of the wire and the applied force were halved, then the increase in its length is