Question

Energy per unit volume of stretched wire is :

• A. $\frac{1}{2}$ $\times$ stress $\times$ strain
• B. stress $\times$ strain
• C. $\frac{1}{2}$ $\times$ load $\times$ strain
• D. load $\times$ strain

Answer 1

Answer: (A)

When a wire is stretched, work is done against the interatomic forces, this work is stored as elastic potential energy in the wire.
Work done = average force $\times$ increase in length
$W=\frac{F}{2}\times l=U$
Let $A$ be area of cross-section of the wire,
then $U=\frac{1}{2}\left(\frac{F}{A}\right)\times \left(\frac{l}{L}\right)\times LA$
$U=\frac{1}{2}\text{stress}\times \text{strain}\times \text{volume of wire}$
Hence, energy per unit volume
$U=\frac{1}{2}\times \text{stress}\times \text{strain}$