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 remaining portion from the centre of mass of the original sphere is:

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$\frac{R}{7}$

$\frac{R}{14}$

$\frac{2 R}{14}$

$\frac{R}{18}$

answer is B.

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Detailed Solution

$x = \frac{m_{2} d}{m_{1} - m_{2}} \Rightarrow x = \frac{r^{3} d}{(R^{3} - r^{3})} \Rightarrow x = \frac{{(\frac{R}{2})}^{3} \frac{R}{2}}{R^{3} - {(\frac{R}{2})}^{3}} \Rightarrow x = \frac{R}{14}$

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