JEE Main 2025 Apr 8 Shift 2, Physics Q10: Measurements

JEE Main2025Apr 8, Shift 2Physics

A quantity $Q$ is formulated as $X^{- 2} Y^{+ 3/2} Z^{- 2/5}$ . $X$ , $Y$ and $Z$ are independent parameters which have fractional errors of $0.1$ , $0.2$ and $0.5$ , respectively in measurement. The maximum fractional error of $Q$ is

A
$0.1$
B
$0.8$
C
$0.7$
D
$0.6$

Solution

For a product-of-powers formula, the maximum fractional error adds contributions from each variable, with each weighted by the magnitude of its exponent.

$\frac{Δ Q}{Q} = ∣ - 2 ∣ \frac{Δ X}{X} + \frac{3}{2} \frac{Δ Y}{Y} + - \frac{2}{5} \frac{Δ Z}{Z}$ .

Substituting: $\frac{Δ Q}{Q} = 2 (0.1) + \frac{3}{2} (0.2) + \frac{2}{5} (0.5) = 0.2 + 0.3 + 0.2 = 0.7$ , matching option (3).

Concept behind this question

MeasurementsNotes, formulas and examples →

Practice more Physics

Concept-wise practice with instant solutions on Fundamenthol.

Start practicing →

JEE Main 2025 Apr 8 Shift 2, Physics Q10: Measurements

Concept behind this question

More previous year questions on Measurements

Practice more Physics