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  4. 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:

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Q. 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:

ManipalManipal 2003Mechanical Properties of Solids

Solution:

When force $F$ is applied $Y=\frac{F L}{A l'}$
where $Y$ is Young's modulus, $A$ is area
$F=\frac{Y A l}{L}$ ...(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)
$F=Y A \times 100\, \alpha$
Hence, force is independent of length $L$