JEE Mains · Physics · STD 11 - Units,dimensions and measurement
- JEE Mains 2025
- Easy
- Numerical
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 _____\(\%\).
Pick an option to check your answer.
Answer & Solution
Correct Answer
(B) 15
Step-by-step Solution
Detailed explanation
\(\mathrm{C}=\mathrm{P}^1 \mathrm{q}^2 \mathrm{r}^{-3} \mathrm{~s}^{1 / 2}\)
\(\left(\frac{\mathrm{dC}}{\mathrm{C}}\right)_{\max }=\frac{\mathrm{dP}}{\mathrm{P}}+\frac{2 \mathrm{dq}}{\mathrm{q}}+\frac{3 \mathrm{dr}}{\mathrm{r}}+\frac{1}{2} \frac{\mathrm{ds}}{\mathrm{s}}\)
\(\begin{aligned}& =\left(1+2 \times 2+3 \times 3+\frac{1}{2} \times 2\right) \% \\& =15 \%\end{aligned}\)
Ans. \(15\)
\(\left(\frac{\mathrm{dC}}{\mathrm{C}}\right)_{\max }=\frac{\mathrm{dP}}{\mathrm{P}}+\frac{2 \mathrm{dq}}{\mathrm{q}}+\frac{3 \mathrm{dr}}{\mathrm{r}}+\frac{1}{2} \frac{\mathrm{ds}}{\mathrm{s}}\)
\(\begin{aligned}& =\left(1+2 \times 2+3 \times 3+\frac{1}{2} \times 2\right) \% \\& =15 \%\end{aligned}\)
Ans. \(15\)
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