Question

In an experiment, the percentage oferror 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 = $\frac{A^2B^{1/2}}{C^{1/3}D^3}$, will be

• A. - 10 %
• B. 10 %
• C. $(\frac{3}{13})$%
• D. 16%

Answer 1

Answer: (D)

Given
$ x =\frac{A^{2}B^{\frac{1}{2}}}{C^{\frac{1}{3}}D^{3}}$
% error, $ \frac{\Delta x}{x} \times100 = 2 \frac{\Delta A}{A} \times100 + \frac{1}{2} \frac{\Delta B}{B} \times 100 + \frac{1}{3} \frac{\Delta c}{c} \times100 + 3 \frac{\Delta D}{D} \times100 $
$ = 2 \times1\% + \frac{1}{2} \times2\% + \frac{1}{3} \times3\% + 3\times4\% $
$ = 2\% + 1\% + 1\% + 12\% $
$= 16\% $