Question

A metal rod length l. Radius of its cross-section is r, its Young's modulus is Y and coefficient of linear expansion is $\alpha$. It is damped between two rigid supports. Now it is heated by ${\theta }^{o}C$. The force exertesd by the bar on any of the supports is

• A. $\pi r^{2}Y\theta$
• B. $\pi r^{2}Y\alpha \theta$
• C. $\pi r^{2}YL\alpha$
• D. $\frac{YL\alpha \theta }{\pi r^2}$

Answer 1

The correct option is B $\pi r^{2}Y\alpha \theta$

$stress=\frac{F}{A}$

$Force=stress$ $\times A$

$=strain\times y\times A$ $\left\{\therefore \frac{\Delta l}{l}=\alpha \theta \right\}$

$=\alpha \theta \times y\times A$

$F=\pi r^{2}y\times \theta$

Hence,

option $\left(B\right)$ is correct answer.