A spherical cavity of radius \( r \) is carved out of a uniform solid sphere of radius \( R \) a...

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A spherical cavity of radius \( r \) is carved out of a uniform solid sphere of radius \( R \) as shown in the figure. The distance of the center of mass of the resulting body from that of the solid sphere is given by
[KVPY 2009]
(a) \( \frac{R-r}{2} \)
(b) 0
(c) \( \frac{R+r}{2} \)
(d) \( \frac{-r^{3}}{R^{2}+R r+r^{3}} \)
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