A physical quantity z depends on four observables a, b, c and d, as z… | JEE Main 2020 (5 Sep, Shift 1)

Q91JEE Main 2020 · 5 SEP · SHIFT 1Medium

Errors in Measurement

A physical quantity z depends on four observables

a, b, c and d, as z = $\frac{a^{2} b^{\frac{2}{3}}}{\sqrt{c}\, d^{3}}$ . The percentages of error in the measurement of a, b, c and d are 2%, 1.5%, 4% and 2.5% respectively. The percentage of error in z is:

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Answer: (b)

$z = \frac{a^2 b^{2/3}}{\sqrt{c}\, d^3} \Rightarrow \frac{\Delta z}{z} = 2\frac{\Delta a}{a} + \frac{2}{3}\frac{\Delta b}{b} + \frac{1}{2}\frac{\Delta c}{c} + 3\frac{\Delta d}{d}$
$= 2(2) + \frac{2}{3}(1.5) + \frac{1}{2}(4) + 3(2.5) = 4 + 1 + 2 + 7.5 = 14.5\%$
So the answer is (b) $14.5\%$ .

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