Question:
A steel rod of length \(5\,\text{m}\) and radius \(2\,\text{cm}\) is heated by \(10^\circ\text{C}\). Find the % change in volume \(\left(\alpha = 10 \times 10^{-6}\,^\circ\text{C}^{-1}\right)\):
A steel rod of length \(5\,\text{m}\) and radius \(2\,\text{cm}\) is heated by \(10^\circ\text{C}\). Find the % change in volume \(\left(\alpha = 10 \times 10^{-6}\,^\circ\text{C}^{-1}\right)\):
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For solids, volumetric expansion coefficient = \(3\alpha\).
Updated On: Jul 18, 2026
- 0.01
- 0.03
- 0.9
- 1.2
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The Correct Option is B
Solution and Explanation
Step 1: Volume expansion relation.
\[ \frac{\Delta V}{V} = 3\alpha \Delta T \]
Step 2: Substitute values.
\[ = 3 \times 10 \times 10^{-6} \times 10 \]
Step 3: Compute.
\[ = 3 \times 10^{-4} \]
Step 4: Convert to percentage.
\[ = 0.03\% \]
Step 5: Interpretation.
This represents fractional volume increase.
Step 6: Final answer.
\[ \boxed{0.03} \]
\[ \frac{\Delta V}{V} = 3\alpha \Delta T \]
Step 2: Substitute values.
\[ = 3 \times 10 \times 10^{-6} \times 10 \]
Step 3: Compute.
\[ = 3 \times 10^{-4} \]
Step 4: Convert to percentage.
\[ = 0.03\% \]
Step 5: Interpretation.
This represents fractional volume increase.
Step 6: Final answer.
\[ \boxed{0.03} \]
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