A physical quantity C is related to four other quantities p, q, r and s as follows The percentage errors in the measurement of p, q, r and s are 1%, 2%, 3% and 2% respectively. The percentage error in the measurement of C will be _______

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Solution

Q.
A physical quantity C is related to four other quantities p, q, r and s as follows

$C = \frac{p q^{2}}{r^{3} \sqrt{s}}$

The percentage errors in the measurement of p, q, r and s are 1%, 2%, 3% and 2% respectively. The percentage error in the measurement of C will be __________ %. [2025]

Ans.
(15)

$C = p^{1} q^{2} r^{- 3} s^{- 1 / 2}$

${(\frac{d C}{C})}_{\max} = \frac{d P}{P} + \frac{2 d q}{q} + \frac{3 d r}{r} + \frac{1}{2} \frac{d s}{s}$

$= (1 + 2 \times 2 + 3 \times 3 + \frac{1}{2} \times 2) % = 15 %$

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