Question

A copper bar of $25cm$ length is fixed by means of supports at its ends. Supports can yield (total) by $0.01cm$. If the temperature of the bar is raised by ${100}^{o}C$, then the stress induced in the bar for ${\alpha }_c=20\times {10}^{-6}{}^{o}C$ and $E_e=1\times {10}^{6}kg/c{m}^2$ will be

• A. $2\times {10}^{2}kg/c{m}^2$
• B. $4\times {10}^{2}kg/c{m}^2$
• C. $8\times {10}^{2}kg/c{m}^2$
• D. $16\times {10}^{2}kg/c{m}^2$

Answer 1

The correct option is D $16\times {10}^{2}kg/c{m}^2$

The elongation in the bar due to increase in temperature $=L\alpha \Delta T$
$\therefore \sigma =\left(\frac{L\alpha \Delta T-\delta }{L}\right)E=E(\alpha \Delta T-\frac{\Delta }{L})$
$=1\times {10}^6\times (20\times {10}^{-6}\times 100-\frac{0.01}{25})$
$=1600kg/c{m}^2$