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A spherical cavity of radius r is carved...

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

A

`(R- r)/(2)`

B

0

C

`(R+ r)/(2)`

D

`(-r^(3))/(R^(2) + Rr + r^(3))`

Text Solution

Verified by Experts

The correct Answer is:
D
`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))`
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