Question

The elastic energy stored in a wire of Youngs modulus $Y$ is

• A. $\frac{1}{2} Y \times$ stress $\times$ strain $\times$ volume
• B. $\frac{(\text { stress })^{2} \times \text { volume }}{2 Y}$
• C. stress $\times$ strain $\times$ volume
• D. $Y \times \frac{(\text { stress })^{2}}{\text { volume }}$

Answer 1

Answer: (B)

When a wire is stretched work is done against the interatomic forces.
This work is stored in the wire in the form of elastic potential energy.
$W=\frac{1}{2} \times$ stress $\times$ strain $\times$ volume of wire
Also when strain is small, ratio of longitudinal stress to corresponding longitudinal strain is called Youngs Modulus of material of body.
$Y =\frac{\text { longitudinal stress }}{\text { longitudinal strain }}$
$\therefore W =\frac{1}{2} \times$ stress $\times \frac{\text { stress }}{ Y } \times$ volume
$=\frac{(\text { stress })^{2} \times \text { volume }}{2 Y}$