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

Options

A. `(R-r)/(2)`
B. 0
C. `(R+r)/(2)`
D. `(-r^(3))/(R^(2)+Rr+r^(3))`

Answer

D

Explanation

`(X=(-m)/(R^(3))r^(3)(R-r))/(m-(mr^(3))/(R^(3)))`
`(-mr^(3)(R-r))/(m(R^(3)-r^(3)))`
= `(-mr^(3)(R-r))/(m(R-r)(R^(2)+Rr+r^(2)))=(-r^(3))/(R^(2)+Rr+r^(3))`