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 $g=10m/s$, 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. $2.5\times 10^{-4}J$

Answer 1

Answer: (B)

$U=\frac{1}{2}\times \frac{(\text{ Stress }{)}^2}{Y}\times \text{ Volume }$
$=\frac{1}{2}\times \frac{F^2\times A\times L}{A^2\times Y}$
$=\frac{1}{2}\times \frac{F^{2}L}{AY}=\frac{1}{2}\times \frac{(50{)}^2\times 0.2}{1\times 10^{-4}\times 1\times 10^{11}}$
$=2.5\times 10^{-5}J$