FIns the centre of mass of a cone and sphere where sphere is kept on top of the hollow cone and also the radius of cone is 2r and height is 4r and radius of the sphere is 2r. Density of material of cone 1/12 times that of sphere. the position of CM on the line of symmetry from the base of the cone is ?

Let the origin at the center of the sphere. 

Center of mass of the cone lies at x distance from the origin. 

so, x = h/4 = 4r/4 = r

Let M and M' be the mass of the cone and the sphere.

Mass of the cone = density of the cone  x volume of the cone

So, the position of the center of mass,

...(i)

on substituting the values in equation (i), you will get the answer.