Question

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`

Answer 1

Correct Answer - B
`((1)/(3)piR^(2)h)pxx(h)/(4)=((2)/(3)piR^(3))p(3R)/(8)`
`h=sqrt(3)R`