JEE Main 2025 Jan 28 Shift 1, Physics Q21: Units And Dimensions

JEE Main2025Jan 28, Shift 1Physics

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 ______

Your answer

Solution

Step 1: least count of the screw gauge.

$LC = \frac{pitch}{number of circular divisions} = \frac{0.75 mm}{15} = 0.05$ mm.

The measurement uncertainty in each length reading is therefore $Δ L = Δ W = 0.05$ mm.

Step 2: fractional error in area.

For $A = L \cdot W$ , the maximum fractional error is

$\frac{Δ A}{A} = \frac{Δ L}{L} + \frac{Δ W}{W} = \frac{0.05}{5} + \frac{0.05}{2.5} = \frac{1}{100} + \frac{2}{100} = \frac{3}{100}$ .

$∴ x = 3$ .

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JEE Main 2025 Jan 28 Shift 1, Physics Q21: Units And Dimensions

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