Question:
A metal tape calibrated at \( 25^\circ C \) is used at \( -15^\circ C \). Coefficient of linear expansion is \( 1 \times 10^{-5}\ /\ ^\circ C \). Find percentage error in measurement.
A metal tape calibrated at \( 25^\circ C \) is used at \( -15^\circ C \). Coefficient of linear expansion is \( 1 \times 10^{-5}\ /\ ^\circ C \). Find percentage error in measurement.
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Length contracts in cold, use \( \Delta L = \alpha L \Delta T \) and express as percent.
Updated On: May 19, 2025
- 0.04%
- 0.05%
- 0.1%
- 0.08%
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The Correct Option is A
Solution and Explanation
\[
\Delta T = 25 - (-15) = 40^\circ C,\quad \Delta L = \alpha \cdot \Delta T
= 1 \times 10^{-5} \cdot 40 = 4 \times 10^{-4}
\]
Percentage error = \( 4 \times 10^{-2}% = 0.04% \)
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