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In an experiment, the percentage of error occurred in the measurement of physical quantities A, B, C and D are 1%, 4%, 3% and 2% respectively. Then the maximum percentage of error in the measurement X where $X = \frac{A^{3} B}{C^{1 / 2} D^{3}}$ will be

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10%

14.5%

14%

-0.5%

answer is C.

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Detailed Solution

$x = \frac{A^{3} B}{C^{1 / 2} D^{3}}$

Maximum percentage error in x

$(\frac{d X}{X}) \times 100 = (3 \frac{d A}{A} + \frac{d B}{B} + \frac{1}{2} \frac{d C}{C} + 3 \frac{d D}{D}) \times 100$

$= 3 \times 1 + 4 + \frac{1}{2} \times 3 + 3 \times 2 = 14.5 %$

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