Question

The volume of a metal sphere increases by $0.15\%,$ when its temperature is raised by ${24}^{\circ }\text{C}$. The coefficient of linear expansion of metal is:

• A. $2.5\times {10}^{-5}{/}^{\circ }\text{C}$
• B. $2.0\times {10}^{-5}{/}^{\circ }\text{C}$
• C. $-1.5\times {10}^{-5}{/}^{\circ }\text{C}$
• D. $1.2\times {10}^{-5}{/}^{\circ }\text{C}$

Answer 1

The correct option is B $2.0\times {10}^{-5}{/}^{\circ }\text{C}$

Coefficient of volumetric expansion
$\gamma =\frac{\Delta V}{V}\times \frac{1}{\Delta T}$
$\gamma =\frac{0.15}{100}\times \frac{1}{24}$
We know that,
Coefficient of linear expansion $\alpha =\frac{\gamma }{3}$
$\alpha =\frac{0.15}{100}\times \frac{1}{24}\times \frac{1}{3}=2.0\times {10}^{-5}{/}^{\circ }C$