A physical quantity P is given as P = a 2 b 3 c d . The percentage error in the measurement of a ,   b …

The given quantity is $P=\frac{a^2{b}^3}{c\sqrt{d}}$.

The percentage error for a quantity can be given by the formula $\frac{∆x}{x}\times 100$.

Relation of the relative errors will be,

$\left(\frac{\Delta P}{P}\right)=\left[\left(\frac{2\Delta a}{a}\right)+\left(\frac{3\Delta b}{b}\right)+\left(\frac{\Delta c}{c}\right)+\left(\frac{1}{2}\frac{\Delta d}{d}\right)\right]$

Hence, the percentage error is calculated by substituting the values,

$\left(\frac{\Delta P}{P}\right)\times 100=\left(2\times 1\right)+\left(3\times 2\right)+3+\left(\frac{1}{2}\times 4\right)=13\%$.