Q 11-10-038NEETJEE MainMedium
A faulty thermometer reads $2°$ in melting ice and $102°$ in steam at normal pressure. When it reads $52°$, the correct temperature on the Celsius scale is
Answer: (A) $50°$C
Concept. Any linear scale gives the same fraction of the way between the fixed points: $\dfrac{C - 0}{100} = \dfrac{x - x_{\text{ice}}}{x_{\text{steam}} - x_{\text{ice}}}$.
Step 1. Substitute.
$$\frac{C}{100} = \frac{52 - 2}{102 - 2} = \frac12 \;\Rightarrow\; C = 50°\text{C}$$
Answer. $50°$C (Option A).
Solution by Sreeraj P, M.Sc Physics