Question

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

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

Answer 1

The correct option is B 16%.

Given,

$X=\frac{A^2{B}^{1/2}}{C^{1/3}{D}^3}$

The percentage relative error in a physical quantity is given by

$\frac{\Delta X}{X}\times 100=2\frac{\Delta A}{A}\times 100+\frac{1}{2}\frac{\Delta B}{B}\times 100+\frac{1}{3}\frac{\Delta C}{C}\times 100+3\frac{\Delta D}{D}\times 100$

% error = $2\times 1\%+\frac{1}{2}\times 2\%+\frac{1}{3}\times 3\%+3\times 4\%$

% error = 16 %.