Question

The volume of a metal sphere increased by $0.24$ % when its temperature is raised by ${40}^{\circ }C$. The coefficient of linear expansion of metal is

• A. $2\times {{10}^{-5}}^{\circ }{C}^{-1}$
• B. $4\times {{10}^{-5}}^{\circ }{C}^{-1}$
• C. $5\times {{10}^{-5}}^{\circ }{C}^{-1}$
• D. $8\times {{10}^{-5}}^{\circ }{C}^{-1}$

Answer 1

The correct option is A $2\times {{10}^{-5}}^{\circ }{C}^{-1}$

We know,
Final volume $V=V_0(1+\gamma \Delta T)$
where $\gamma$ is coefficient of volumetric expansion
$\frac{\Delta V}{V_0}=\gamma \Delta T$
% Change in volume $\frac{\Delta V}{V_0}\times 100=\gamma \Delta T\times 100$
$\Rightarrow 0.24=\gamma \times 40\times 100$
$\therefore \gamma =6\times {{10}^{-5}}^{\circ }{C}^{-1}$

Also,we know,
$\alpha =\frac{\gamma }{3}$
where $\alpha$ is coefficient of linear expansion
$\therefore \alpha =\frac{6\times {{10}^{-5}}^{\circ }{C}^{-1}}{3}$
$=2\times {{10}^{-5}}^{\circ }{C}^{-1}$