A right circular cone of radius `R` and height `2 R` is placed on a hemisphere of radius `R`. Locate `c.m.` of the combined mass from `O`.

Explanation

Cone : `m_(1) prop (1)/(3) pi R^(2) ( 2R) rArr m_(1) = (k xx 2 pi R^(3))/(3) , y_(1) = ( 2R)/(4) = (R )/(2)`
`m_(2) prop (2)/(3) pi R^(3) rArr m_(2) = (k xx 2 pi R^(3))/(3) , y_(2) = -(3 R)/(8)`
`m_(1) = m_(2) = m`
`y_(c.m.) = (m_(1) y_(1) + m_(2) y_(2))/(m_(1) + m_(2)) = ((R )/(2) - ( 3R)/(8))/(1 + 1) = (R )/(16)`