Question

A steel rod of length area of cross-section $A$, Young's modulus $Y$ and coefficient of linear expansion a is heated through $t^o$ C. The work done that can be performed by the rod now is :

• A. $YA\frac {\alpha\,t} {l} $
• B. $ \frac 12 (YA \alpha t) (l \alpha t)$
• C. $\frac {1}{2} (YA \alpha t) (\frac {t}{2} l \alpha t)$
• D. $2(YA \alpha t) (l \alpha t )$

Answer 1

Answer: (B)

Work done = $\frac{1}{2} \times Force \times Change\, in\, length = \frac{1}{2} (YA\propto t) (l\propto\,t)$