A physical quantity C is related to four other quantities p, q, r and… | JEE Main 2025 (3 Apr, Shift 2)

Q55JEE Main 2025 · 3 APR · SHIFT 2Medium

Errors in Measurement

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

$C = \frac{pq^{2}}{r^{3}\sqrt{s}}$

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__________%

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

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Answer: 15

$C = \frac{p q^2}{r^3 \sqrt{s}} \Rightarrow \frac{\Delta C}{C} = \frac{\Delta p}{p} + 2\frac{\Delta q}{q} + 3\frac{\Delta r}{r} + \frac{1}{2}\frac{\Delta s}{s}$
$= 1 + 2(2) + 3(3) + \frac{1}{2}(2) = 1 + 4 + 9 + 1 = 15\%$
Answer: $15\%$ .

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