Question

A steel rod of length l, area of cross section A, Young's modulus E and linear coefficient of expansion a is heated through $t^{\circ }C$. The work that can be performed by the rod when heated is

• A. $\left(EAat\right)\times \left(lat\right)$
• B. $\frac{1}{2}\left(EAat\right)\times \left(lat\right)$
• C. $\frac{1}{2}\left(EAat\right)\times \frac{1}{2}\left(lat\right)$
• D. $2\left(EAat\right)\left(lat\right)$

Answer 1

Answer: (B)

$\frac{1}{2}\left(EAat\right)\times \left(lat\right)$

Work done = Energy stored = $1/2\times Stress\times Strain\times Volume=1/2\times \left(Eat\right)\times \left(at\right)\times Al$, which is given is option B.