Question

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

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

Answer 1

Answer: (B)

Linear expansion coefficient $\alpha=\frac{\gamma}{3}=\frac{1}{3} .\frac{\Delta V}{V \Delta t} $
$\Rightarrow \alpha=\frac{1}{3} \cdot \frac{0.15}{100 \times 24}$
$ \Rightarrow \alpha=2 \times 10^{-5} /{ }^{\circ} C$