Question

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

• A. ${10}^{-5}$ joule
• B. $2.5\times {10}^{-5}$ joule
• C. $5\times {10}^{-5}$ joule
• D. $2.5\times {10}^{-4}$ joule

Answer 1

Answer: (B)

$2.5\times {10}^{-5}$ joule

$U=\frac{1}{2}F\Delta l$

$\Delta l=\frac{FL}{YA}$

$U=\frac{1}{2}\frac{F^{2}L}{YA}=\frac{1}{2}\times \frac{{50}^2\times 0.2}{{10}^{11}\times {10}^{-4}}=2.5\times {10}^{-5}J$