JEE Mains · Physics · STD 11 - Units,dimensions and measurement
- JEE Mains 2024
- Hard
- MCQ
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 \(\mathrm{Q}\) is _______.
Pick an option to check your answer.
Answer & Solution
Correct Answer
(C) \(34 \%\)
Step-by-step Solution
Detailed explanation
\( \mathrm{Q}=\frac{\mathrm{a}^4 \mathrm{~b}^3}{\mathrm{c}^2} \)
\( \frac{\Delta \mathrm{Q}}{\mathrm{Q}}=4 \frac{\Delta \mathrm{a}}{\mathrm{a}}+3 \frac{\Delta \mathrm{b}}{\mathrm{b}}+2 \frac{\Delta \mathrm{c}}{\mathrm{c}} \)
\( \frac{\Delta \mathrm{Q}}{\mathrm{Q}} \times 100=4\left(\frac{\Delta \mathrm{a}}{\mathrm{a}} \times 100\right)+3\left(\frac{\Delta \mathrm{b}}{\mathrm{b}} \times 100\right)+2\left(\frac{\Delta \mathrm{c}}{\mathrm{c}} \times 100\right) \)
\( \% \text { error in } \mathrm{Q}=4 \times 3 \%+3 \times 4 \%+2 \times 5 \% \)
\(=12 \%+12 \%+10 \% \)
\(=34 \%\)
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