A uniform solid right circular cone has its base cut out in conical shape shown in figure such that the hollow portion is a right circular cone on the same base. Find what should be the height of the hollow portion so that the centre of mass of the remaining portion may coincide with the vertex of the hollow portion.

Options

A. `h/3`
B. `h/4`
C. `(2h)/3`
D. `h/6`

Answer

A

Explanation

`M = rho 1/3 pi r^2 h, Y_(CM) = (h)/(4) " [Before removed)"`
`M = rho 1/3 pi r^2 h_1, Y_(1_(CM)) = (h_1)/(4) " [For removed part)"`
`Y_(CM) = h_1 = (M_Y - M_1 Y_1)/(M - M_1)`
`=(rho 1/3 pir^2((h^2)/4 - (h_1^2)/(4)))/(rho1/3 pi r^2 (h - h_1)) implies h_1 = (h_1 + h)/(4) implies h_1 = h/3`