Q. An iron bar of length $l$ and having a cross-section $A$ is heated from 0 to $100℃$. If this bar is so held that it is not permitted to expand or bend, the force that is developed, is
A) Inversely proportional to the cross-sectional area of the bar
B) Independent of the length of the bar
C) Inversely proportional to the length of the bar
D) Directly proportional to the length of the bar
Explanation
(b) $Y = \frac{FL}{Al}$ where $Y$ is Young’s modulus, $A$ is area
$\Rightarrow F = \frac{YAl}{L}$ $\ldots(i)$
From the formula for linear expansion
$\alpha = \frac{l}{L \times 100}$ $\ldots(ii)$
According to the condition the bar should not bend or expand
Now from equations (i) and (ii)
$F = YA \times 100\alpha$
Hence, force is independent of length $L$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.