Question

A metallic rod of length $l$ and cross–sectional area A is made of a material of Young’s modulus $Y$. if the rod is elongated by an amount $y$, then the work done is proportional to

• A. $y$
• B. $\frac{1}{y}$
• C. $y^2$
• D. $\frac{1}{y^2}$

Answer 1

The correct option is C $y^2$


$W.D=\frac{1}{2}\times \mathrm{stress}\times strain\times volume$

strain $=\frac{y}{l}$

Stress $=Y\times$ strain = $Y\frac{y}{l}$

Volume=$A\times l$
$⟹W.D=\frac{1}{2}\frac{YA}{l}{y}^2$