Question

A physical quantity $x$ is represented as $x=M^2{L}^3{T}^{-1}$, and maximum percentage errors in $M,L$ & $T$ are 1%, 2% and 1% respectively, then maximum percentage error in $x$ is

• A. 7%
• B. 8%
• C. 9%
• D. 5%

Answer 1

The correct option is C 9%

$\frac{\Delta x}{x}=2\frac{\Delta M}{M}+3\frac{\Delta L}{L}+1\frac{\Delta T}{T}$
$\frac{\Delta x}{x}\%=2\times 1\%+3\times 2\%+1\times 1\%=(2+6+1)\%\Rightarrow \frac{\Delta x}{x}\%=9\%$