Question

An iron bar whose cross sectional area is $4c{m}^2$ is heated from $0^{\circ }C$ and ${100}^{\circ }C$. The force required to prevent the expansion of the rod is :
(Y of Iron = $2\times {10}^{12}dyne/c{m}^2$, $\alpha$ of Iron = $12\times {10}^6{/}^{\circ }C$)

• A. $0.96\times {10}^{8}N$
• B. $0.96\times {10}^{7}N$
• C. $9.6\times {10}^{7}N$
• D. $192\times {10}^{3}N$

Answer 1

The correct option is D $192\times {10}^{3}N$

$Y=\frac{\frac{F}{A}}{\frac{\Delta A}{A}}=\frac{\frac{F}{A}}{A\frac{2\alpha \Delta T}{A}}=\frac{\frac{F}{A}}{2\alpha \Delta T}$

$\Rightarrow F=2YA\alpha \Delta T$

$=2\times (2\times {10}^{12}\times {10}^{-5}\times {10}^4)\times (4\times {10}^{-4})\times (12\times {10}^{-6})\times (100-0)$

$=192\times {10}^{3}N$