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In the measurement of a physical quantity $X = \frac{A^{2} B}{C^{1 / 3} D^{3}}$ . The percentage errors introduced in the measurements of the quantities A,B,C and D are 2%, 2%, 4% and 5% respectively. Then the minimum amount of percentage of error in the measurement of X is contributed by

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answer is C.

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Detailed Solution

$\begin{array}{l} \frac{ΔX}{X} \times 100 = 2 \frac{ΔA}{A} \times 100 + \frac{ΔB}{B} \times 100 \\ + \frac{1}{3} \frac{ΔC}{C} \times 100 + \frac{3 ΔD}{D} \times 100 \end{array}$

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