A brass wire of cross-sectional area $2 {\mathrm{mm}}^2$ is suspended from a rigid support and body of volume $100 {\mathrm{cm}}^3$ is attached to its other end. If the decrease in the length of the wire is $0.11 \mathrm{mm}$, when the body is completely immersed in water, find the natural length of the wire.

$\left(Y_{brass}=0.91\times {10}^{11} \mathrm{N} {\mathrm{m}}^{-2}, {\rho }_{\mathit{w}\mathit{a}\mathit{t}\mathit{e}\mathit{r}}=1000 \mathrm{kg} {\mathrm{m}}^{-3}, g=9.8 \mathrm{m} {\mathrm{s}}^{-2}\right)$

Two wires of different material have same lengths and areas of cross-section. What is the ratio of their increase in length when forces applied are the same?

$\left(Y_1=0.9\times {10}^{11} \mathrm{N} {\mathrm{m}}^{-2}, Y_2=3.6\times {10}^{11} \mathrm{N} {\mathrm{m}}^{-2} \right)$

An aluminium Wire and a steel wire of the same length and cross-section are joined end-to-end. The composite wire is hung from a rigid support and a load is suspended from the free end. If the increase in length of the composite wire is $1.35 \mathrm{mm}$, find the ratio of the (i) stress in the two wires and (ii) strain in the two wires. 

$\left(Y_{Al}=0.7\times {10}^{11} \mathrm{N} {\mathrm{m}}^{-2}, Y_{steel}=2\times {10}^{11} \mathrm{N} {\mathrm{m}}^{-2}\right)$

A copper cube of side of length $1 \mathrm{cm}$ is subjected to a pressure of $100 \mathrm{atmosphere}$. Find the change in its volume if the bulk modulus of copper is $1.4\times {10}^{11} \mathrm{N} {\mathrm{m}}^{-2}$. 

$\left(1 \mathrm{atmosphere}=1\times {10}^5 {\mathrm{Nm}}^{-2}\right)$