Question

A brass rod of cross-sectional area $1c{m}^2$ and length $0.2m$ is compressed lengthwise by a weight of $5kg$. If Young's modulus of elasticity of brass is $1\times {10}^{11}N/m^2$ and $g=10m/se{c}^2$, then increase in the energy of the rod will be:

• A. ${10}^{-5}J$
• B. $2.5\times {10}^{-5}J$
• C. $5\times {10}^{-5}J$
• D. $2.5\times {10}^{11}J$

Answer 1

The correct option is B $2.5\times {10}^{-5}J$

$\text{Elastic potential evergy stored}\left(u\right)=\frac{1}{2}\times \text{stress}x\text{strain}x\text{volume}$

$\begin{array}{c}Y=\frac{\text{stress}}{\text{str}ain}\\ \text{strain}=\frac{\text{Stress}}{y}\end{array}$

$\begin{array}{cc}U& =\frac{1}{2}\times \frac{(\text{Stress}{)}^2}{Y}\times V\cdot 0\text{frod}\\ & =\frac{1}{2}\times \frac{F^2}{A^{2}Y}\times \left(Kh\right)\\ & =\frac{1}{2}\times \frac{F^2}{AY}\times h\\ & =\frac{1}{2}\times \frac{\left(2500\right)}{1\times {10}^{-4}\times {10}^{11}}\times 0.2m\\ & =2.5\times {10}^{-5}J\end{array}$

Hence option B is correct