$A$ wire of cross-sectional area $3 \, mm^2$ is first stretched between two fixed points at a temperature of $20^{\circ}C$. Determine the tension in the wire when the temperature falls to $10^{\circ}C$. Given: Coefficient of linear expansion $\alpha = 10^{-5} \, ^{\circ}C^{-1}$ and Young's modulus $Y = 2 \times 10^{11} \, N/m^2$.

Young's modulus of elasticity of a material depends upon

Under the same load,wire $A$ having length $5.0 \, m$ and cross-section $2.5 \times 10^{-5} \, m^2$ stretches uniformly by the same amount as another wire $B$ of length $6.0 \, m$ and a cross-section of $3.0 \times 10^{-5} \, m^2$ stretches. The ratio of the Young's modulus of wire $A$ to that of wire $B$ will be

$A$ steel ring of radius $r$ and cross-section area $A$ is fitted onto a wooden disc of radius $R$ $(R > r)$. If Young's modulus is $E$,then the force with which the steel ring is expanded is

$A$ uniformly tapering conical wire is made from a material of Young's modulus $Y$ and has a normal,unextended length $L$. The radii at the upper and lower ends of this conical wire have values $R$ and $3R$,respectively. The upper end of the wire is fixed to a rigid support and a mass $M$ is suspended from its lower end. The equilibrium extended length of this wire would be:

$A$ steel ring of radius '$r$' is to be fitted over a wooden disc of radius '$R$' $(R > r)$. The force required to expand the ring so that it fits over the disc is ($Y =$ Young's modulus of steel,$A =$ area of cross-section of the wire).