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} $