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JEE Main 2022 (25 Jun, Shift 2) · Errors in Measurement

Errors in Measurement question from JEE Main 2022 (25 Jun, Shift 2)

Q77JEE Main 2022 · 25 JUN · SHIFT 2Medium

Errors in Measurement

For $z = a^{2} x^{3} y^{\frac{1}{2}}$ , where 'a' is a constant. If percentage error in measurement of 'x' and 'y' are 4% and 12% respectively, then the percentage error for 'z' will be _______________%.

Numerical answer type. Work it out, then open the answer.

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Answer: 18

$z = a^2 x^3 y^{1/2}$ with $a$ constant, so $\frac{\Delta z}{z} = 3\frac{\Delta x}{x} + \frac{1}{2}\frac{\Delta y}{y}$
$= 3(4) + \frac{1}{2}(12) = 12 + 6 = 18\%$
Answer: $18\%$ .

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