JEE Main 2025 Apr 3 Shift 2, Physics Q25: Measurements

JEE Main2025Apr 3, Shift 2Physics

A physical quantity $C$ is related to four other quantities $p$ , $q$ , $r$ and $s$ as follows

$C = \frac{p q ^{2}}{r ^{3} s}$

The percentage errors in the measurement of $p$ , $q$ , $r$ and $s$ are $1%$ , $2%$ , $3%$ and $2%$ respectively. The percentage error in the measurement of $C$ will be _________ %.

Your answer

Solution

For a product/quotient of powers, fractional uncertainties add in absolute value, weighted by the exponents:

$\frac{Δ C}{C} = \frac{Δ p}{p} + 2 \frac{Δ q}{q} + 3 \frac{Δ r}{r} + \frac{1}{2} \frac{Δ s}{s}$ .

Substituting the given percentages:

$\frac{Δ C}{C} \times 100 = 1 + 2 \cdot 2 + 3 \cdot 3 + \frac{1}{2} \cdot 2 = 1 + 4 + 9 + 1 = 15%$ .

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JEE Main 2025 Apr 3 Shift 2, Physics Q25: Measurements

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