Mathematics in Physics

JEE Main level, numerical answer, medium

58 of 121

Question 58 of 121

A physical quantity C is related to four other quantities p,q,r\mathrm{p}, \mathrm{q}, \mathrm{r} and s as follows C=pq2r3 s\mathrm{C}=\frac{\mathrm{pq}^2}{\mathrm{r}^3 \sqrt{\mathrm{~s}}}
The percentage errors in the measurement of p,q,r\mathrm{p}, \mathrm{q}, \mathrm{r} and s are 1%,2%3%1 \%, 2 \% 3 \% and 2%2 \% respectively.
The percentage error in the measurement of C will be _____%\%.

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Answer: 15

C=P1q2r−3 s1/2\mathrm{C}=\mathrm{P}^1 \mathrm{q}^2 \mathrm{r}^{-3} \mathrm{~s}^{1 / 2}
(dCC)max⁡=dPP+2dqq+3drr+12dss\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}}
=(1+2×2+3×3+12×2)%=15%\begin{aligned}& =\left(1+2 \times 2+3 \times 3+\frac{1}{2} \times 2\right) \% \\& =15 \%\end{aligned}
Ans. 1515

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