A physical quantity P is given as . The percentage error in the measurement of a, b, c and d are 1%, 2%, 3% and 4% respectively. The percentage error in the measurement of quantity P will be [2023]

Question

A physical quantity P is given as $P = \frac{a^{2} b^{3}}{c \sqrt{d}}$ . The percentage error in the measurement of a, b, c and d are 1%, 2%, 3% and 4% respectively. The percentage error in the measurement of quantity P will be [2023]

Smart Achievers · Accepted Answer

(1)

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

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

Solution

Q.
A physical quantity P is given as $P = \frac{a^{2} b^{3}}{c \sqrt{d}}$ . The percentage error in the measurement of a, b, c and d are 1%, 2%, 3% and 4% respectively. The percentage error in the measurement of quantity P will be [2023]

1 13%

2 14%

3 12%

4 16%

Ans.
(1)

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

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

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