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Offline Centres

Find coordinates of center of mass of a quarter sector of a uniform disk of radius $r$ placed in the first quadrant of a Cartesian coordinate system with centre at origin.

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$(\frac{4 r}{3 π}, \frac{4 r}{3 π})$

$(\frac{4 r}{π}, \frac{4 r}{3 π})$

$(\frac{r}{π}, \frac{4 r}{3 π})$

$(\frac{r}{3 π}, \frac{r}{3 π})$

answer is A.

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Detailed Solution

From the result obtained for sector of circular plate distance $O C$ of the center of mass form the center is

$O C = \frac{2 r \sin (π / 4)}{3 π / 4} = \frac{4 \sqrt{2} r}{3 π}$

Coordinates of the center of mass $(x_{c}, y_{c})$ are $(\frac{4 r}{3 π}, \frac{4 r}{3 π})$

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