Question

A physical quantity $P$ depends on $\alpha ,\beta $ and $\gamma $ as $P=\frac{\alpha ^{2} \beta }{\gamma ^{4}}.$ If the percentage error in the measurement of $\alpha ,\beta $ and $\gamma $ are respectively $0.1\%,0.2\%$ and $0.4\%,$ then the maximum percentage error in the measurement of $P$ is

• A. $1.2\%$
• B. $1.5\%$
• C. $2.0\%$
• D. $2.6\%$

Answer 1

Answer: (C)

$P=\alpha ^{2}\frac{\beta }{\gamma ^{4}}$
$\Rightarrow \frac{\Delta P}{P}\times 100$
$=2\left(\frac{\Delta \alpha }{\alpha } \times 100\right)+\left(\frac{\Delta \beta }{\beta } \times 100\right)+4\left[\frac{\Delta \gamma }{\gamma } \times 100\right]$
$=2\left[\right.0.1\left]\right.+0.2+4\left[\right.0.4\left]\right.$
$=0.2+0.2+1.6=2.0\%$