Q 11-10-039NEETJEE MainEasy
A steel scale is correct at $0°$C. A length measured with it at $40°$C reads $50.00$ cm. If $\alpha_{steel} = 1.2 \times 10^{-5}\ °\text{C}^{-1}$, the true length is
Answer: (B) $50.024$ cm
Concept. At $40°$C each scale division has expanded, so the true length is the reading times $(1 + \alpha\Delta T)$.
Step 1. Substitute.
$$L = 50(1 + 1.2 \times 10^{-5} \times 40) = 50 \times 1.00048 = 50.024\ \text{cm}$$
Answer. $50.024$ cm (Option B).
Solution by Sreeraj P, M.Sc Physics