A tiny metallic rectangular sheet has length and breadth of 5 mm and… | JEE Main 2025 (28 Jan, Shift 1)

Q12JEE Main 2025 · 28 JAN · SHIFT 1Medium

Least Count, Vernier Callipers & Screw Gauge

A tiny metallic rectangular sheet has length and breadth of 5 mm and 2.5 mm, respectively. Using a specially designed screw gauge which has pitch of 0.75 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 $\frac{x}{100}$ where $x$ is _______.

Numerical answer type. Work it out, then open the answer.

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Answer: 3

LC $= \dfrac{0.75}{15} = 0.05\text{ mm}$ , so $\Delta l = \Delta b = 0.05\text{ mm}$
$A = lb \Rightarrow \dfrac{\Delta A}{A} = \dfrac{\Delta l}{l} + \dfrac{\Delta b}{b}$
$= \dfrac{0.05}{5} + \dfrac{0.05}{2.5} = 0.01 + 0.02 = \dfrac{3}{100}$
So $x = 3$ .

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