Question 82: Units , Dimensions and Error Analysis

Question

A physical quantity $$Q$$ is found to depend on quantities $$a, b, c$$ by the relation $$Q=\frac{a^4 b^3}{c^2}$$. The percentage error in $$a, b$$ and $$c$$ are $$3 \%, 4 \%$$ and $$5 \%$$ respectively. Then, the percentage error in $$Q$$ is :

Accepted Answer

$$\begin{aligned}
& \mathrm{Q}=\frac{\mathrm{a}^4 \mathrm{~b}^3}{\mathrm{c}^2} \
& \frac{\Delta \mathrm{Q}}{\mathrm{Q}}=4 \frac{\Delta \mathrm{a}}{\mathrm{a}}+3 \frac{\Delta \mathrm{b}}{\mathrm{b}}+2 \frac{\Delta \mathrm{c}}{\mathrm{c}}
\end{aligned}$$
$$\frac{\Delta \mathrm{Q}}{\mathrm{Q}} 	imes 100=4\left(\frac{\Delta \mathrm{a}}{\mathrm{a}} 	imes 100ight)+3\left(\frac{\Delta \mathrm{b}}{\mathrm{b}} 	imes 100ight)+2\left(\frac{\Delta \mathrm{c}}{\mathrm{c}} 	imes 100ight)$$
$$\begin{aligned}
\% 	ext { error in } \mathrm{Q} & =4 	imes 3 \%+3 	imes 4 \%+2 	imes 5 \% \
& =12 \%+12 \%+10 \% \
& =34 \%
\end{aligned}$$

Answer

43%

Answer

34%

Answer

66%

Answer

14%

Units , Dimensions and Error Analysis

A physical quantity $Q is found to depend on quantities a, b, c by the relation Q=\frac{a^4 b^3}{c^2}. The percentage error in a, b and c are 3 \%, 4 \% and 5 \% respectively. Then, the percentage error in Q$ is :

Choose the correct answer: