A physical quantity $P$ is related to four observations $a,b,c$ and $d$ as follows:$$P = a^{3}b^{2}/

Question

A physical quantity $P$ is related to four observations $a,b,c$ and $d$ as follows:

$$P = a^{3}b^{2}/c\sqrt{d}$$

The percentage errors of measurement in $a,b,c$ and $d$ are $1\%,3\%,2\%$, and $4\%$ respectively. The percentage error in the quantity $P$ is

Accepted Answer

Maximum % error in $P = \frac{\Delta P}{P} \times 100$

$$= 3\left( \frac{\Delta a}{a} \times 100 \right) + 2\left( \frac{\Delta b}{b} \times 100 \right) + \left( \frac{\Delta c}{c} \times 100 \right) + \frac{1}{2}\left( \frac{\Delta d}{d} \times 100 \right)$$

$$\begin{matrix} & \ = 3 \times (1) + 2 \times (3) + (2) + \frac{1}{2} \times (4) \\ & \ = 13\% \end{matrix}$$

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