Q 11-01-231JEE MainJEE Main 2018 (16 Apr, Shift 1)Easy
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 $A = \dfrac{P^3Q^2}{\sqrt R\,S}$. The maximum percentage error in the value of $A$ will be:
Answer: (A) $6.5\%$
Maximum relative errors add, each weighted by its power:
$$\frac{\Delta A}{A} = 3\frac{\Delta P}{P} + 2\frac{\Delta Q}{Q} + \frac12\frac{\Delta R}{R} + \frac{\Delta S}{S}$$
$$= 3(0.5) + 2(1) + \tfrac12(3) + 1.5 = 1.5 + 2 + 1.5 + 1.5 = 6.5\%$$
Solution by Sreeraj P, M.Sc Physics