Q 11-01-031NEETJEE MainTop questionMedium
A physical quantity is calculated as $Q = \dfrac{a^2 b^3}{c\sqrt{d}}$. The percentage errors in measuring $a$, $b$, $c$ and $d$ are $1\%$, $2\%$, $3\%$ and $4\%$ respectively. The maximum percentage error in $Q$ is
Answer: (B) $13\%$
For a product of powers, multiply each percentage error by its power (ignore signs) and add:
$$\frac{\Delta Q}{Q}\times 100 = 2(1) + 3(2) + 1(3) + \tfrac12(4) = 2 + 6 + 3 + 2 = 13\%$$
Notice that $b$, with the largest power, contributes the most error. That's the quantity to measure most carefully.
Solution by Sreeraj P, M.Sc Physics