In an experiment, the percentage of error occurred in the measurement of physical quantities A, B, C and D are 1%, 2%, 3% and 4%, respectively. The maximum percentage of error in the measurement X, where , will be [2019]

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Solution

Q.
In an experiment, the percentage of error occurred in the measurement of physical quantities A, B, C and D are 1%, 2%, 3% and 4%, respectively. The maximum percentage of error in the measurement X, where $X = \frac{A^{2} B^{1 / 2}}{C^{1 / 3} D^{3}}$ , will be [2019]

1 10%

2 $(\frac{3}{13}) %$

3 16%

4 -10%

Ans.
(3)

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

Maximum percentage error in X

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

$= 2 \times 1 + \frac{1}{2} \times 2 + \frac{1}{3} \times 3 + 3 \times 4 = 16 %$

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