Q 11-01-171JEE MainJEE Main 2021 (27 Jul, Shift 2)Medium
A physical quantity $y$ is represented by the formula $y = m^2r^{-4}g^xl^{-\frac32}$. If the percentage errors found in $y$, $m$, $r$, $l$ and $g$ are $18$, $1$, $0.5$, $4$ and $p$ respectively, then find the value of $x$ and $p$.
Answer: (C) $\dfrac{16}{3}$ and $\pm\dfrac32$
$$\frac{\Delta y}{y} = 2\frac{\Delta m}{m} + 4\frac{\Delta r}{r} + x\frac{\Delta g}{g} + \frac32\frac{\Delta l}{l}$$
$18 = 2(1) + 4(0.5) + xp + \dfrac32(4) = 10 + xp \Rightarrow xp = 8$.
Only option (3) satisfies this: $\dfrac{16}{3}\times\dfrac32 = 8$.
Solution by Sreeraj P, M.Sc Physics