Question

When the temperature of a metal sphere increases by ${100}^{\circ }C$, its surface area increases by 0.2%. Coefficient of cubical expansion of the sphere is :

• A. $5\times {10}^{-6}{/}^{\circ }C$
• B. $10\times {10}^{-6}{/}^{\circ }C$
• C. $20\times {10}^{-6}{/}^{\circ }C$
• D. $30\times {10}^{-6}{/}^{\circ }C$

Answer 1

Answer: (D)

$30\times {10}^{-6}{/}^{\circ }C$

In this case, dt $=$ Change in temperature $={100}^{\circ }$C
$dA=$ Change in area $=0.2$%
We know $\beta =\frac{changeinarea}{originalarea\times changeintemperature}$

Putting change in area $=$ 0.2 $m^2$, original area $=$ 100 $m^2$ and $dt={100}^{\circ }$C
we get, $\beta =2\times {10}^{-5}{/}^{\circ }$C
Now, $\gamma =\left(3/2\right)\beta$
So, we get $\gamma =30\times {10}^{-6}{/}^{\circ }$C