Centre of mass is the point at which the entire mass of the object is concentrated. The cone can be either a solid cone or a hollow cone. The hollow cone will have the centre of mass at a distance of 2h/3 from the apex and at a distance of h/3 from the base.
Let us determine the value of the centre of mass (centre of gravity) of a hollow cylinder.
Let us consider a hollow cone of height H. A circular ring of thickness dx is considered at a height y from the base of the cone. The radius of the ring is taken as x sinθ.
Area of the circular ring, dA = 2π(xsinθ)dx
Mass of the circular ring of thickness dx is,
dM = 2Mxdx/(R2 +H2)——–(1)
y = H – xcosθ
Centre of mass,
Substitute the values from equa (1) and equa (2) in equa (3) and integrate it
Solving the above equation we get C = H/3
Centre of Mass of the hollow cone, C = H/3
Where H is the height of the cone.