The volume of a metal block increases by $0.225 \%$ when its temperature is increased by $30^{\circ}…
The volume of a metal block increases by $0.225 \%$ when its temperature is increased by $30^{\circ} \mathrm{C}$. Hence coefficient of linear expansion of the material of metal block is
$7.5 \times 10^{-5} /{ }^{\circ} \mathrm{C}$.
$6.75 \times 10^{-5} /{ }^{\circ} \mathrm{C}$.
$2.5 \times 10^{-5} /{ }^{\circ} \mathrm{C}$.
$1.5 \times 10^{-5} /{ }^{\circ} \mathrm{C}$.
Solution
The increase in volume is $\frac{\Delta V}{V} \times 100=0.225$ Change in temperature is $\Delta \mathrm{T}=30^{\circ} \mathrm{C}$ We know, $\gamma=3 \alpha$
$\therefore \quad$ The change in volume is $\Delta \mathrm{V}=\mathrm{V} \gamma \Delta \mathrm{T}$
$\begin{array}{ll}
\therefore & \frac{\Delta V}{\mathrm{~V}} \times 100=3 \alpha \Delta \mathrm{T} \times 100 \\
\therefore & 0.225=3 \alpha \times 30 \times 100 \\
\therefore & \alpha=\frac{0.225}{3 \times 30 \times 100} \\
\therefore & \alpha=2.5 \times 10^{-5} /{ }^{\circ} \mathrm{C}
\end{array}$