Question

The dimensional formula for a physical quantity $X$ is $\left(M^{-1}{L}^3{T}^{-2}\right]$. The errors in measuring the quantities $M$, $L$ and $T$, are 2%, 3%, and 4% respectively. The maximum percentage of error that occurs in measuring the quantity $X$ is

Answer 1

$X=M^{-1}{L}^3{T}^{-2}$
Taking log and differentiating and adding all errors as errors are always added and never subtracted, we get
$\frac{\Delta X}{X}=\frac{\Delta M}{M}+3\frac{\Delta L}{L}+2\frac{\Delta T}{T}$
$=\frac{2}{100}+3\times \frac{3}{100}+2\times \frac{4}{100}=\frac{19}{100}$
$\Rightarrow \frac{\Delta X}{X}\times 100=19$.
Therefore, maximum percentage error is 19.