A physical quantity C is related to four other quantities $\mathrm{p}, \mathrm{q}, \mathrm{r}$ and s as follows $\mathrm{C}=\frac{\mathrm{pq}^2}{\mathrm{r}^3 \sqrt{\mathrm{~s}}}$
The percentage errors in the measurement of $\mathrm{p}, \mathrm{q}, \mathrm{r}$ and s are $1 \%, 2 \% 3 \%$ and $2 \%$ respectively.
The percentage error in the measurement of C will be _____$\%$.

Question

Aicharya · Accepted Answer

$\mathrm{C}=\mathrm{P}^1 \mathrm{q}^2 \mathrm{r}^{-3} \mathrm{~s}^{1 / 2}$
$\left(\frac{\mathrm{dC}}{\mathrm{C}}\right)_{\max }=\frac{\mathrm{dP}}{\mathrm{P}}+\frac{2 \mathrm{dq}}{\mathrm{q}}+\frac{3 \mathrm{dr}}{\mathrm{r}}+\frac{1}{2} \frac{\mathrm{ds}}{\mathrm{s}}$
$\begin{aligned}& =\left(1+2 \times 2+3 \times 3+\frac{1}{2} \times 2\right) \% \\& =15 \%\end{aligned}$
Ans. $15$

A physical quantity C is related to four other quantities $\mathrm{p}, \mathrm{q}, \mathrm{r}$ and s as…

Solution