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A physical quantity S is related to four observables a, b, c, d as $S = \frac{\sqrt{a} b}{c^{3} d^{4}}$ .If the percentage errors of measurement in a, b, c, d are 2%, 1%, 1% and 1% respectively, then percentage error in the quantity S is

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Detailed Solution

We have

$S= \frac{\sqrt{a} b}{c^{3} d^{4}}$ $\frac{ΔS}{S} = \frac{1}{2} \frac{Δa}{a} + \frac{Δb}{b} - \frac{3Δc}{c} - \frac{4Δd}{d}$

$|\frac{ΔS}{S} × 100| = |\frac{1}{2} × 2%| + |1%| + |3 × 1%| + |4 × 1%|$

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