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 = $\frac{A^2{B}^{1/2}}{C^{1/3}{D}^3}$, 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, $\frac{\Delta x}{x}\times 100=2\frac{\Delta A}{A}\times 100+\frac{1}{2}\frac{\Delta B}{B}\times 100+\frac{1}{3}\frac{\Delta c}{c}\times 100+3\frac{\Delta D}{D}\times 100$
$=2\times 1\%+\frac{1}{2}\times 2\%+\frac{1}{3}\times 3\%+3\times 4\%$
$=2\%+1\%+1\%+12\%$
$=16\%$