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 $16\%$

$X=\frac{A^2{B}^{1/2}}{C^{1/3}{D}^3}\frac{\Delta X}{X}=2\frac{\Delta A}{A}+\frac{1}{2}\frac{\Delta B}{B}+\frac{1}{3}\frac{\Delta C}{C}+3\frac{\Delta D}{D}\Rightarrow \frac{\Delta X}{X}\times 100=2\left(1\%\right)+\frac{1}{2}\left(2\%\right)+\frac{1}{3}\left(3\%\right)+3\left(4\%\right)=16\%$