MHT CET · Physics · Thermal Properties of Matter
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
- A \(7.5 \times 10^{-5} /{ }^{\circ} \mathrm{C}\).
- B \(6.75 \times 10^{-5} /{ }^{\circ} \mathrm{C}\).
- C \(2.5 \times 10^{-5} /{ }^{\circ} \mathrm{C}\).
- D \(1.5 \times 10^{-5} /{ }^{\circ} \mathrm{C}\).
Answer & Solution
Correct Answer
(C) \(2.5 \times 10^{-5} /{ }^{\circ} \mathrm{C}\).
Step-by-step Solution
Detailed explanation
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 \(\Delta \mathrm{V}=\mathrm{V} \gamma \Delta \mathrm{T}\)
\(
\begin{array}{ll}
\therefore & \frac{\Delta V}{\mathrm{~V}} \times 100=3 \alpha \Delta \mathrm{T} \times 100 \\
\therefore & 0.225=3 \alpha \times 30 \times 100 \\
\therefore & \alpha=\frac{0.225}{3 \times 30 \times 100} \\
\therefore & \alpha=2.5 \times 10^{-5} /{ }^{\circ} \mathrm{C}
\end{array}
\)
\(\therefore \quad\) The change in volume is \(\Delta \mathrm{V}=\mathrm{V} \gamma \Delta \mathrm{T}\)
\(
\begin{array}{ll}
\therefore & \frac{\Delta V}{\mathrm{~V}} \times 100=3 \alpha \Delta \mathrm{T} \times 100 \\
\therefore & 0.225=3 \alpha \times 30 \times 100 \\
\therefore & \alpha=\frac{0.225}{3 \times 30 \times 100} \\
\therefore & \alpha=2.5 \times 10^{-5} /{ }^{\circ} \mathrm{C}
\end{array}
\)
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