When a block of mass $M$ is suspended by a long wire of length $L$ and cross-sectional area $A$, the

Question

When a block of mass $M$ is suspended by a long wire of length $L$ and cross-sectional area $A$, the length of the wire becomes $(L+l)$. The elastic potential energy stored per unit volume in the extended wire is

Professor PC Thomas Classes · Answer

Stress in the wire is $\sigma = \frac{F}{A} = \frac{Mg}{A}$. Strain in the wire is $\epsilon = \frac{\Delta L}{L} = \frac{l}{L}$. The elastic potential energy density (energy stored per unit volume) is given by $u = \frac{1}{2} 	imes 	ext{Stress} 	imes 	ext{Strain} = \frac{1}{2} \left(\frac{Mg}{A}ight) \left(\frac{l}{L}ight) = \frac{Mgl}{2AL}$.