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A uniform solid right circular cone of b...

A uniform solid right circular cone of base radius `R` is joined to a uniform solid hemisphere of radius `R` and of the same density, as shown. The centre of mass of the composite solid lies at the centre of base of the cone. The height of the cone is

A

`1.5R`

B

`sqrt(3)R`

C

`3R`

D

`2sqrt(3)R`

Text Solution

Verified by Experts

The correct Answer is:
B
`y_(CM)=(m_1y_1+m_2y_2)/(m_1+m_2)`
`=(rhox1/3piR^2hxxh/4=rhoxx2/3piR^3xx(3R)/8)/(rhoxx1/3piR^2h+rhoxx2/3piR^3)`

`impliesh=sqrt3R`
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