If error in measuring diameter of a circle is 4% , error in radius of circle would be

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1.Units, Dimensions and Measurement

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If error in measuring diameter of a circle is $4\%$, the error in radius of the circle would be

A

$2$

B

$8$

C

$4$

D

$1$

Solution

radius $\left( {\text{r}} \right)\, = \,\frac{1}{2}\, \times \,$ diameter $\left( D \right)$

$dr\, = \,\frac{1}{2}\,\,dD\,\Rightarrow \,\frac{{dr}}{r}\, = \,\frac{1}{2}\,\frac{{dD}}{{\frac{1}{2}D}}\,$

$\, \Rightarrow \,\frac{{dr}}{r}\, \times \,100\, = \,\frac{{dD}}{D}\, \times \,100\, = \,4\% $

Standard 11

Physics

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