Question

A quantity is represented by $X=M^a{L}^b{T}^c$. The $\%$ error in measurement of $M$, $L$ and $T$ are $\alpha$%, $\beta$% and $\gamma$% respectively. The maximum $\%$ error in $X$ would be:

• A. $(\alpha a+\beta b+\gamma c)\%$
• B. $(\alpha a-\beta b+\gamma c)\%$
• C. $(\alpha a-\beta b+\gamma c)\times 100\%$
• D. none of these

Answer 1

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

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

So, maximum error:

$\frac{\Delta X}{X}\times 100=(\frac{a\Delta M}{M}+\frac{b\Delta L}{L}+\frac{c\Delta T}{T})\times 100$$=(\alpha a+\beta b+\gamma c)$%