Question

A physical quantity is given by $X=\left[M^a{L}^b{T}^c\right]$. The percentage error in measurement of $M,L$ and $T$ are $\alpha ,\beta$ and $\gamma$ respectively. Then, the maximum % error in the quantity X is

• A. $a\alpha +b\beta +c\gamma$
• B. $a\alpha +b\beta -c\gamma$
• C. $\frac{a}{\alpha }+\frac{b}{\beta }+\frac{c}{\gamma }$
• D. None of these

Answer 1

The correct option is A $a\alpha +b\beta +c\gamma$

$X=\left[M^a{L}^b{T}^c\right]$

On differentiating we get
Maximum % error in $X$
$=a\alpha +b\beta +c\gamma$