Question

A steel rod is streched along its length by $1\text{mm}$. The rod has initial length as $1\text{m}$ and cross sectional area $0.01{\text{m}}^2$. Young's modulus of steel is $2\times {10}^{11}\text{Pa}$. The potential energy stored in the steel rod assuming negligible change in volume due to streching of the rod is (in $\text{J}$):

• A. $10$
• B. $100$
• C. $1000$
• D. $10000$

Answer 1

The correct option is C $1000$

The elatic energy stored is $\Delta U=\frac{1}{2}\times Y\times (\text{strain}{)}^2\times \text{volume}$
$\Delta U=\frac{1}{2}\times 2\times {10}^{11}\times {\left(\frac{0.001}{1}\right)}^2\times 0.01$
$\Delta U=1000\text{J}$