Question

A steel tape of 300 cm is graduated at \( 27^\circ \text{C} \). A steel rod measured to be 110 cm at \( 50^\circ \text{C} \) with this tape has actual length (given \( \alpha_{\text{steel}} = 1.2 \times 10^{-5} \, \text{K}^{-1} \)):

• A. \( 110.03 \, \text{cm} \)
• B. \( 110.10 \, \text{cm} \)
• C. \( 110.07 \, \text{cm} \)
• D. \( 110.62 \, \text{cm} \)

Hint:

Always apply thermal expansion correction when measurement device expands with temperature.

Answer 1

The Correct Option is A

Since tape expands, it overestimates length. Correction:
\[ L_{\text{actual}} = L_{\text{measured}} \cdot \left(1 + \alpha \Delta T\right)
= 110 \cdot \left(1 + 1.2 \times 10^{-5} \cdot (50 - 27)\right) = 110 \cdot (1 + 2.76 \times 10^{-4}) = 110.03 \, \text{cm} \]