Question

A physical quantity is represented by $x=M^a{L}^b{T}^{-c}.$ If the percentage of error in the measurements of $M,L,T$ are $\alpha$% , $\beta$% and $\gamma$% then the maximum percentage error in $x$ is :

• A. $a\alpha +b\beta +c\gamma$
• B. $a^{\alpha }+b^{\beta }+c^{\gamma }$
• C. $a\alpha \times b\beta \times c\gamma$
• D. $a^{\alpha }\times b^{\beta }\times c^{\gamma }$

Answer 1

Answer: (A)

$a\alpha +b\beta +c\gamma$

Given, $x=M^a{L}^b{T}^{-c}$

So, $\frac{\Delta x}{x}=\pm (a\frac{\Delta M}{M}+b\frac{\Delta L}{L}+c\frac{\Delta T}{T})$

The maximum % error, $\frac{\Delta x}{x}\times 100=(a\frac{\Delta M}{M}\times 100+b\frac{\Delta L}{L}\times 100+c\frac{\Delta T}{T}\times 100)=a\alpha +b\beta +c\gamma$