$A$ wire of length $50\, cm$ and cross-sectional area of $1\, mm^2$ is extended by $1\, mm$. The required work done will be $(Y = 2 \times 10^{10}\, N/m^2)$.

Two wires of the same material and length but diameters in the ratio $1:2$ are stretched by the same force. The elastic potential energy per unit volume for the wires,when stretched by the same force,will be in the ratio: (in $:1$)

Work done by the restoring force in a string within the elastic limit is $-10 \, J$. The maximum amount of heat produced in the string is .......... $J$.

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

$A$ uniform rod of length $L$ has a mass per unit length $\lambda$ and area of cross-section $A$. If the Young's modulus of the rod is $Y$,then the elongation in the rod due to its own weight is:

$A$ steel rod of length $\ell$,cross-sectional area $A$,Young's modulus of elasticity $Y$,and thermal coefficient of linear expansion $\alpha$ is heated so that its temperature increases by $t\,^\circ C$. The work that can be done by the rod on heating is: