Two steel wires having same length are suspended from a ceiling under the same load. If the ratio of their energy stored per unit volume is $1: 4$,the ratio of their diameters is

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 .......... $J$.

$A$ wire of initial length $L$ and radius $r$ is stretched by a length $l$. Another wire of same material but with initial length $2L$ and radius $2r$ is stretched by a length $2l$. The ratio of stored elastic energy per unit volume in the first and second wire is

$A$ wire of length $L$ and area of cross-section $A$ is made of a material with Young's modulus $Y$. It is stretched by an amount $x$. The work done in stretching the wire is:

Which of the following is true for elastic potential energy density?

$A$ wire of length $1 \, m$ and Young's modulus $Y = 2.0 \times 10^{11} \, N/m^2$ is fixed between two rigid supports. If its temperature is increased by $100 ^\circ C$,what is the energy stored in the wire? (Given: $\alpha = 18 \times 10^{-6} \, ^\circ C^{-1}$,$A = 1 \, cm^2$)