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As shown in figure, when a spherical cav...

As shown in figure, when a spherical cavity (centered at O) of radius 2 is cut out of a uniform sphere of radius R (centered at C), the centre of mass of remaining (shaded) part of sphere is at G, i.e, on the surface of the cavity. R can be determined by the equation:

A

`(R^2 - 2 R+4)(4-R)=8`

B

`(R^2 + 2R-4)(4-R)=8`

C

`(R^2 + 2 R+4)(4-4)=8`

D

`(R^2-2 R-4)(4-R)=8`

Text Solution

Verified by Experts

The correct Answer is:
C
By concept of COM
`m_1 R_1 = m_2R_2`
Remaining mass `xx` (4-R) = Cavity mass `xx`(R-2)
`(4/3piR^2 rho-4/3 pi2^3 rho)(4-R)=4/3 pi2^3 rho xx(Rxx2)`
`(R^2 + 2R+4)(4-R)=8`
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