A physical quantity P is related to four observations a, b, c and d as follows: The percentage errors of measurement in a, b, c and d are 1%, 3%, 2% and 4% respectively. The percentage error in the quantity P is: [2025]

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Solution

Q.
A physical quantity P is related to four observations a, b, c and d as follows: $P = \frac{a^{3} b^{2}}{c \sqrt{d}}$

The percentage errors of measurement in a, b, c and d are 1%, 3%, 2% and 4% respectively. The percentage error in the quantity P is: [2025]

1 13%

2 15%

3 10%

4 2%

Ans.
(1)

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

Percentage error in quantity P,

$\frac{Δ P}{P} \times 100 = (\frac{3 Δ a}{a} + \frac{2 Δ b}{b} + \frac{Δ c}{c} + \frac{1}{2} \frac{Δ d}{d}) \times 100$

$= 3 (1) + 2 (3) + 2 + \frac{1}{2} \times 4 = 3 + 6 + 2 + 2 = 13 %$

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