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

(\frac{3}{13}) %

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16 %

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- 10 %

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10 %

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Solution

The correct option is B $16 %$
$X = \frac{A^{2} B^{1 / 2}}{C^{1 / 3} D^{3}} \frac{Δ X}{X} = 2 \frac{Δ A}{A} + \frac{1}{2} \frac{Δ B}{B} + \frac{1}{3} \frac{Δ C}{C} + 3 \frac{Δ D}{D} \Rightarrow \frac{Δ X}{X} \times 100 = 2 (1 %) + \frac{1}{2} (2 %) + \frac{1}{3} (3 %) + 3 (4 %) = 16 %$

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In an experiment, the percentage of error occured in the measurement of physical quantities A, B, C and D are 1%, 2%, 3% and 4 % respectively. Then, the maximum percentage of error in the measurement of X, where X = A2B1/2C1/3D3, will be

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

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