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A uniform sphere has radius R. A sphere of diameter R is cut from its edge as shown. Then the distance of centre of mass of the remaining portion from the centre of mass of the original sphere is

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R/18

2R/7

R/14

R/7

answer is B.

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Detailed Solution

$R_{1} = R$ , $R_{2} = \frac{R}{2}$ ; $d = R_{1} - R_{2} = \frac{R}{2}$

For sphere, $m \propto R^{3}$

$x_{c m}$ of remaining portion from centre of original sphere

$x_{c m} = \frac{r_{2}^{3} (r_{1} - r_{2})}{r_{1}^{3} - r_{2}^{3}} = \frac{\frac{R^{3}}{8} (R - \frac{R}{2})}{R^{3} - \frac{R^{3}}{8}} = \frac{R}{14}$

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