Question

A physical quantity $X$ is given by $X=\frac{2k^3{l}^2}{m\sqrt{n}}$ The percentage error in the measurements of $k,l,m$ and $n$ are $1\%,2\%,3\%$ and $4\%$ respectively. The value of $X$ is uncertain by

• A. 8%
• B. 10%
• C. 12%
• D. None of these

Answer 1

Answer: (C)

Given : $X=\frac{2k^3{1}^2}{m\sqrt{n}}$
$\therefore \frac{\Delta X}{X}=3\frac{\Delta k}{k}+2\frac{\Delta 1}{1}+\frac{\Delta m}{m}+\frac{1}{2}\frac{\Delta n}{n}$
Percentage error in $X$
$\frac{\Delta X}{X}\times 100=\left(3\frac{\Delta k}{k}+2\frac{\Delta 1}{1}+\frac{\Delta m}{m}+\frac{1}{2}\frac{\Delta n}{n}\right)\times 100$
$=3\times 1\%+2\times 2\%+3\%+\frac{1}{2}\times 4\%$
$=3\%+4\%+3\%+2\%=12\%$
Hence, the value of $X$ is uncertain by $12\%$.