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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%, 2%, 3% and 4% respectively. Then the maximum percentage of error in the measurement X, where $X = (A^{2}B^{1/2})/(C^{1/3}D^{3})$ will be:
Explanation
Given, $X = A^{2}B^{1/2}/(C^{1/3}D^{3})$ % error, $\Delta x/x \times 100 = 2(\Delta A/A) \times 100 + (1/2)(\Delta B/B) \times 100 + (1/3)(\Delta C/C) \times 100 + 3(\Delta D/D) \times 100$ = $2 \times 1\% + (1/2) \times 2\% + (1/3) \times 3\% + 3 \times 4\% = 2\% + 1\% + 1\% + 12\% = 16\%$