Question

An iron bar of length $l$ and having a cross-section A is heated from $0^{\circ }$ to $100^{\circ }$ . 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

Answer 1

Answer: (B)

When force $F$ is applied $Y=\frac{FL}{A{l}^{\prime }}$
where $Y$ is Young's modulus, $A$ is area
$F=\frac{YAl}{L}$ ...(1)
From the formula for linear expansion
$\alpha =\frac{l}{L\times 100}$ ...(2)
According to the condition that bar will not bend or expand
Now from equations (1) and (2)
$F=YA\times 100\alpha$
Hence, force is independent of length $L$