Mathematics In Physics Question 4
Question 4 - 2024 (29 Jan Shift 2)
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 :
(1) $66 \%$
(2) $43 \%$
(3) $34 \%$
(4) $14 \%$
Show Answer
Answer: (3)
Solution:
$Q=\frac{a^{4} b^{3}}{c^{2}}$
$\frac{\Delta Q}{Q}=4 \frac{\Delta a}{a}+3 \frac{\Delta b}{b}+2 \frac{\Delta c}{c}$
$\frac{\Delta Q}{Q} \times 100=4\left(\frac{\Delta a}{a} \times 100\right)+3\left(\frac{\Delta b}{b} \times 100\right)+2\left(\frac{\Delta c}{c} \times 100\right)$
$$ \begin{aligned} \% \text { error in } Q & =4 \times 3 \%+3 \times 4 \%+2 \times 5 \% \\ & =12 \%+12 \%+10 \% \\ & =34 \% \end{aligned} $$
