In an experiment four quantities a, b, c and d are measured with percentage error 1%, 2%, 3% and 4% respectively. Quantity P is calculated as follows P = (a3 b2/cd) % error in P is :-

Question

In an experiment four quantities a, b, c and d are measured with percentage error 1%, 2%, 3% and 4% respectively. Quantity P is calculated as follows P = (a3 b2/cd) % error in P is :- (A) 4 % (B) 14 % (C) 10 % (D) 7 %

Tardigrade Admin · Accepted Answer

P = (a3 b2/ cd) (Δ P/P) = ± (3 (Δ a/a) + 2(Δ b/b) + (Δ c/c) + (Δ d/d)) = ±(3 × 1 + 2 × 2 + 3+ 4) =± 14 %

Q. In an experiment four quantities a, b, c and d are measured with percentage error 1%, 2%, 3% and 4% respectively. Quantity P is calculated as follows $P = \frac{a ^{3} b ^{2}}{c d}$ % error in P is :-

4 %

14 %

10 %

7 %

P = $\frac{a ^{3} b ^{2}}{c d} \frac{Δ P}{P} = \pm (3 \frac{Δ a}{a} + 2 \frac{Δ b}{b} + \frac{Δ c}{c} + \frac{Δ d}{d})$
$= \pm (3 \times 1 + 2 \times 2 + 3 + 4)$
= $\pm 14$

Q. In an experiment four quantities a, b, c and d are measured with percentage error 1%, 2%, 3% and 4% respectively. Quantity P is calculated as follows P=cda3b2​ % error in P is :-

4 %

14 %

10 %

7 %

P = cda3b2​PΔP​=±(3aΔa​+2bΔb​+cΔc​+dΔd​) =±(3×1+2×2+3+4) =±14

Q. In an experiment four quantities a, b, c and d are measured with percentage error 1%, 2%, 3% and 4% respectively. Quantity P is calculated as follows $P = \frac{a ^{3} b ^{2}}{c d}$ % error in P is :-

P = $\frac{a ^{3} b ^{2}}{c d} \frac{Δ P}{P} = \pm (3 \frac{Δ a}{a} + 2 \frac{Δ b}{b} + \frac{Δ c}{c} + \frac{Δ d}{d})$
$= \pm (3 \times 1 + 2 \times 2 + 3 + 4)$
= $\pm 14$