Q88 / 90 · JEE Main 2018 (16 Apr Online) · Physics

The percentage errors in quantities $P$ , $Q$ , $R$ and $S$ are $0.5 %$ , $1 %$ , $3 %$ and $1.5 %$ respectively in the measurement of a physical quantity $A= \frac{P^{3} Q^{2}}{\sqrt{R} S}$ . The maximum percentage error in the value of $A$ will be:

Correct answer
A
$6.5 %$
B
$7.5 %$
C
$6.0 %$
D
$8.5 %$

Solution

100 \times (\frac{∆ A}{A}) = (\frac{3 ∆ P}{P} + \frac{2 ∆ Q}{Q} + \frac{1}{2} \frac{∆ R}{R} + \frac{∆ S}{S}) \times 100

max percentage error,

A = 3 \times 0.5 + 2 \times 1 + \frac{1}{2} \times 3 + 1.5

= 1.5 + 2 + 1.5 + 1.5

= 6.5 %

Hence, the correct answer is option: 'A'.

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