Question

A physical quantity $\varrho$ is related to four independent observables $\alpha ,\beta ,$ c and d as $\varrho =\frac{{\alpha }^3{\beta }^2}{\sqrt{cd}}$.The percentage error of measurment in $\alpha ,\beta$ , c and d respectively are $1\%,3\%,4\%$ and $2\%$ .The percentage error in the quantity $\varrho$ is then

• A. $5\%$
• B. $12\%$
• C. $13\%$
• D. $24\%$

Answer 1

The correct option is B $12\%$

Physical quantity is given as $\rho =\frac{{\alpha }^3{\beta }^2}{\sqrt{cd}}$
Percentage error in the quantity $\frac{\Delta \rho }{\rho }=3\frac{\Delta \alpha }{\alpha }+2\frac{\Delta \beta }{\beta }+\frac{1}{2}\frac{\Delta c}{c}+\frac{1}{2}\frac{\Delta d}{d}$
$\therefore$ $\frac{\Delta \rho }{\rho }=3\left(1\right)+2\left(3\right)+0.5\left(4\right)+0.5\left(2\right)=12$ %