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1.Units, Dimensions and Measurement
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In an experiment four quantities $a, b, c$ and $d$ are measured with percentage error $1\%, 2\%, 3\%$ and $4\%$ respectively. Quantity $P$ is calculated as follows $P = \frac{{{a^3}{b^2}}}{{cd}}$ $\%$ error in the measurement of $P$ is .......... $\%$
A
$4$
B
$14$
C
$10$
D
$7$
Solution
$\begin{aligned} \mathrm{P}=\frac{\mathrm{a}^{3} \mathrm{b}^{2}}{\mathrm{cd}} \Rightarrow & \frac{\Delta \mathrm{P}}{\mathrm{P}}=\pm\left(3 \frac{\Delta \mathrm{a}}{\mathrm{a}}+2 \frac{\Delta \mathrm{b}}{\mathrm{b}}+\frac{\Delta \mathrm{c}}{\mathrm{c}}+\frac{\Delta \mathrm{d}}{\mathrm{d}}\right) \\ &=\pm(3 \times 1+2 \times 2+3+4) \\ &=\pm 14 \% \end{aligned}$
Standard 11
Physics
