JEE Main 2026 Apr 6 Shift 2, Physics Q1: Measurements

JEE Main2026Apr 6, Shift 2Physics

The percentage error in the calculated volume of a sphere, if there is 2% error in its diameter measurement, is ____.

Solution

Volume of a sphere: $V = \frac{4}{3} π R^{3}$ , so the relative error multiplies by 3:

$\frac{Δ V}{V} = 3 \frac{Δ R}{R} = 3 \frac{Δ D}{D}$

With $\frac{Δ D}{D} = 2%$ , we get $\frac{Δ V}{V} = 6%$ .

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