A physical quantity P is given as P = a² b³c√(d) The percentage error… | JEE Main 2023 (10 Apr, Shift 1)

Q71JEE Main 2023 · 10 APR · SHIFT 1Medium

Errors in Measurement

A physical quantity P is given as

$P = \frac{a^{2} b^{3}}{c\sqrt{d}}$

The percentage error in the measurement of a, b, c and d are 1%, 2%, 3% and 4% respectively. The percentage error in the measurement of quantity P will be

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Answer: (b)

$P = \frac{a^2 b^3}{c\sqrt{d}} \Rightarrow \frac{\Delta P}{P} = 2\frac{\Delta a}{a} + 3\frac{\Delta b}{b} + \frac{\Delta c}{c} + \frac{1}{2}\frac{\Delta d}{d}$
$= 2(1) + 3(2) + 3 + \frac{1}{2}(4) = 2 + 6 + 3 + 2 = 13\%$
So the answer is (b) $13\%$ .

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