Q 11-01-083JEE MainJEE Main 2025 (28 Jan, Shift 1)Medium
A tiny metallic rectangular sheet has length and breadth of $5\ \text{mm}$ and $2.5\ \text{mm}$, respectively. Using a specially designed screw gauge which has a pitch of $0.75\ \text{mm}$ and 15 divisions in the circular scale, you are asked to find the area of the sheet. In this measurement, the maximum fractional error will be $\dfrac{x}{100}$ where $x$ is ______.
Numerical value type. Enter your answer.
Answer: 3
Least count $= \dfrac{0.75}{15} = 0.05\ \text{mm}$; this is the error in each length.
For $A = lb$:
$$\frac{\Delta A}{A} = \frac{\Delta l}{l} + \frac{\Delta b}{b} = \frac{0.05}{5} + \frac{0.05}{2.5} = 0.01 + 0.02 = \frac{3}{100}$$
$x = 3$
Solution by Sreeraj P, M.Sc Physics