Question

A brass rod of cross section 2 cm X 2 cm is heated through ${10}^{\circ }C$ and prevented from expansion. The thermal force exerted on the clamp is :
(For brass, $\alpha =2\times {10}^{-5}{/}^{\circ }C$ and $Y=2\times {10}^{10}Pa$)

• A. 160 N
• B. 1600 N
• C. 100 N
• D. 8000 N

Answer 1

Answer: (B)

1600 N

$Y=\frac{\frac{F}{A}}{\frac{\Delta L}{L}}$
$\therefore F=YA\frac{\Delta L}{L}=YA\alpha \Delta T$
$F=(2\times {10}^{10})\times (4\times {10}^{-4})(2\times {10}^{-5}\times (10-0\left)\right)=8\times {10}^6\times (2\times {10}^{-4})=1600N$

Hence, the thermal force exerted on the clamp is 1600 N