Question

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

• A. $16:1$
• B. $4:1$
• C. $2:1$
• D. $1:1$

Answer 1

The correct option is A $16:1$

Potential energy per unit volume = $\frac{1}{2}\times Stress\times Strain=\frac{1}{2}\times \frac{{\left(Stress\right)}^2}{Y}$

Since same material, thus Y will be same. Thus it is linearly proportional to ${\left(Stress\right)}^2$ or ${\left(\frac{F}{A}\right)}^2$

Thus it is inversely proportional to square of area or radii to power 4. Thus, ratio will be ${\left(1/2\right)}^{-4}=16:1$