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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 $w$ is calculated as follows $w\, = \,\frac{{{a^4}{b^3}}}{{{c^2}\sqrt D }}$ error in the measurement of $w$ is .......... $\%$
A
$10$
B
$16$
C
$18$
D
$12$
Solution
$\frac{{\Delta W}}{W}\,\, = \,\,4\,\frac{{\Delta a}}{a}\,\, + \,\,3\,\frac{{\Delta b}}{b}\, + \,\,2\frac{{\Delta c}}{c}\,\, + \,\,\frac{1}{2}\,\,\frac{{\Delta d}}{d}$
$ = 4(1\% ) + 3(2\% )\, + 2(3\% )\, + \,\frac{1}{2}(4\% ) = 18\,\% $
Standard 11
Physics