A physical quantity Q is found to depend on quantities a, b, c by the relation Q = (a⁴b³)/(c²). The percentage error in a, b and c are 3%, 4% and 5% respectively. Then, the percentage error in Q is: (a) 43% (b) 34% (c) 66% (d) 14%

Answer: (b). For Q = (a⁴b³)/(c²): (Δ Q)/(Q) = 4(Δ a)/(a) + 3(Δ b)/(b) + 2(Δ c)/(c) = 4(3) + 3(4) + 2(5) = 12 + 12 + 10 = 34% So the answer is (b) 34%.

A physical quantity Q is found to depend on quantities a, b, c by the… | JEE Main 2024 (29 Jan, Shift 2)

Q60JEE Main 2024 · 29 JAN · SHIFT 2Easy

Errors in Measurement

A physical quantity $Q$ is found to depend on quantities $a, b, c$ by the relation $Q = \frac{a^4b^3}{c^2}$ . The percentage error in $a, b$ and $c$ are $3\%, 4\%$ and $5\%$ respectively. Then, the percentage error in $Q$ is:

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Answer: (b)

For $Q = \frac{a^4b^3}{c^2}$ : $\frac{\Delta Q}{Q} = 4\frac{\Delta a}{a} + 3\frac{\Delta b}{b} + 2\frac{\Delta c}{c}$
$= 4(3) + 3(4) + 2(5) = 12 + 12 + 10 = 34\%$
So the answer is (b) 34%.

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Errors in Measurement question from JEE Main 2024 (29 Jan, Shift 2)

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