A physical quantity P is related to four observables a, b, c, d as follows: P = $P = \frac{a^{3} b^{2}}{(\sqrt{c}, d)}$ The percentage errors in the measurement of a, b, c and d are $1 % 3 % 4 % a n d 2 %$ respectively. The percentage error in the quantity P is

%

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Solution

The correct option is D 13 $%$
P = $a^{3} b^{2} . c^{- \frac{1}{2}} . d^{- 1} ∣ ∣ \frac{Δ P}{P} ∣ ∣ = 3 ∣ ∣ (\frac{Δ a}{a}) ∣ ∣ + 2 ∣ ∣ (\frac{Δ b}{b}) ∣ ∣ + \frac{1}{2} ∣ ∣ \frac{Δ c}{c} ∣ ∣ + ∣ ∣ \frac{Δ d}{d} ∣ ∣ \Rightarrow Percentage error in P = 3 (1 %) + 2 (3 %) + \frac{1}{2} (4 %) + 2 % = (3 + 6 + 2 + 2) % = 13 %$

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A physical quantity P is related to four observables a, b, c, d as follows: P = P=a3b2(√c,d) The percentage errors in the measurement of a, b, c and d are 1%3%4%and2% respectively. The percentage error in the quantity P is

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