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1.Units, Dimensions and Measurement
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In an experiment, the percentage of error occurred in the measurment of physical quantities $A, B, C$ and $D$ are $1 \%, 2 \%, 3 \%$ and $4 \%$ respectively. Then the maximum percentage of error in the measurement $X,$
where $X = \frac{{{A^2}{B^{\frac{1}{2}}}}}{{{C^{\frac{1}{3}}}{D^3}}}$, will be
A
$\left(\frac{3}{13}\right) \%$
B
$16 \%$
C
$-10 \%$
D
$10 \%$
(NEET-2019)
Solution
$\mathrm{x}=\frac{\mathrm{A}^{2} \mathrm{B}^{1 / 2}}{\mathrm{C}^{1 / 3} \mathrm{D}^{3}}$
$\frac{\Delta x}{x}=\frac{2 \Delta A}{A}+\frac{1}{2} \frac{\Delta B}{B}+\frac{1}{3} \frac{\Delta C}{C}+3 \frac{\Delta D}{D}$
$\frac{\Delta x}{x} \times 100=2(1 \%)+\frac{1}{2}(2 \%)+\frac{1}{3}(3 \%)+3(4 \%)=16 \%$
Standard 11
Physics
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