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1.Units, Dimensions and Measurement
easy
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 $P$ is ........ $\%$
A
$14$
B
$10$
C
$7$
D
$4$
(AIPMT-2013)
Solution
As, $P = \frac{{{a^3}{b^2}}}{{cd}}$
$ \% $, error, in, $P$, is
$\frac{{\Delta P}}{P} \times 100 = \left[ {3\left( {\frac{{\Delta a}}{a}} \right) + 2\left( {\frac{{\Delta b}}{b}} \right) + \frac{{\Delta c}}{c} + \frac{{\Delta d}}{d}} \right] \times 100$
$ = 3\left[ {3 \times 1\% + 2 \times 2\% + 3\% + 4\% } \right] = 14\% $
Standard 11
Physics
