Question

At $0^{\circ }C$, a square steel bar of $1cm$ side, is rigidly clamped at both ends so that its length cannot increase. Young's modulus of steel is $20\times {10}^{10}N{m}^{-2}$ and its coefficient of linear expansion is $11\times {10}^{-6}{/}^{\circ }C$. When the temperature is raised to ${10}^{\circ }C$ , the force exerted on the clamp is

• A. $1100N$
• B. $2200N$
• C. $3300N$
• D. $4400N$

Answer 1

The correct option is B $2200N$

Length, $l=1cm=0.01m$
Change in temperature $=dt=10$ [change in temperature in degree kelvin is same as degree centigrade]
$Y=stress/strain$
$=\left(F/A\right)/dl/l$
Now, $\alpha =dl/\left(ldt\right)$
or, $dl=l\alpha dt$
Putting the value of dl we get,
$Y=F/\left(\alpha dtA\right)$
Or, $F=Y\alpha dtA$
Putting value of $\alpha =11$ X ${10}^{-6}$, $Y=20$ X ${10}^{10}$, dt = 10 and A = $(0.01{)}^2$
We get force as $22\times {10}^2$ N