Q127 / 180 · NEET 2025 · Physics
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
- A$10 \%$
- B$2 \%$
- Correct answerC$13 \%$
- D$15 \%$
Solution
$\begin{aligned} & P=a^3 b^2 c^{-1} d^{-1 / 2} \\ & \left(\frac{\Delta P}{P} \times 100\right)=\left(\frac{3 \Delta a}{a}+\frac{2 \Delta b}{b}+\frac{1 \Delta c}{c}+\frac{1}{2} \frac{3 \Delta d}{d}\right) \times 100 \\ & =3(1 \%)+2(3 \%)+1(2 \%)+\frac{1}{2}(4 \%) \\ & =13 \%\end{aligned}$
Hence, the correct answer is option: 'C'.