Question

The length of a rod is $20cm$ and area of cross-section $2c{m}^2$ . The Young's modulus of the material of wire is $1.4\times {10}^{11}N{m}^{-2}$. If the rod is compressed by $5kg-wt$ along its length, then increase in the energy of the rod in joules will be

• A. $8.57\times {10}^{-6}J$
• B. $22.5\times {10}^{-4}J$
• C. $9.8\times {10}^{-5}J$
• D. $45.0\times {10}^{-5}J$

Answer 1

The correct option is A

$8.57\times {10}^{-6}J$

$\Delta U=\frac{1}{2}\times Force\times elongation$

$=\frac{1}{2}\times F\times \left(\frac{FL}{AY}\right)$

$=\frac{1}{2}\times \frac{F^{2}L}{AY}$

$=\frac{1}{2}\times \frac{(5\times 9.8{)}^2\times 20\times {10}^{-2}}{2\times {10}^{-4}\times 1.4\times {10}^{11}}$

$=8.57\times {10}^{-6}J$