Question

A physical quantity is given by $X=M^a{L}^b{T}^c$. 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

Answer: (A)

$X=M^a{L}^b{T}^c$
Percentage error in X
$\frac{\Delta X}{X}\times 100=a\frac{\Delta M}{M}\times 100+b\frac{\Delta L}{L}\times 100+c\frac{\Delta T}{T}\times 100$ As given,
$\frac{\Delta M}{M}\times 100=\alpha ,\frac{\Delta L}{L}\times 100=\beta ,\frac{\Delta T}{T}\times 100=\gamma$
$\therefore$ Percentage error in $X=a\alpha +b\beta +c\gamma .$