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The radius of sphere is measured to be $(2.1 \pm 0.5)$ cms. What is its surface area with error limits?
jeemain
physics
class11
units-and-measurement
ch2
accuracy-precision-and-errors-in-measurement
easy
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Jul 11, 2014
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balaji.thirumalai
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Surface area $S= 4\pi r^2 = 4 \pi (2.1)^2 = 55.4\;cm^2$
$\Rightarrow \large\frac{\Delta S}{S}$$ = 2 \large\frac{\Delta r}{r}$$ \rightarrow \Delta S = 2 \large\frac{\Delta r}{r}$$S$
$\Rightarrow \Delta S = \large\frac{2 \times 0.5 \times 55.4}{2.1}$$ = 26.4 \;cm^2$
$\Rightarrow S = 55.4 \pm 26.4 cm^2$
answered
Jul 11, 2014
by
balaji.thirumalai
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