Center of Mass of solid cone

The centre of mass of a solid cone along the line form the center of the base to the vertex is at

Distance of the centre of mass of a solid uniform cone from its vertex is z_0 . It the radius of its base is R and its height is h then z_0 is equal to:

A uniform solid cone of height 40 cm is shown in figure. The distance of centre of mass of the cone from point B (centre of the base) is :

A vessel, in the form of an inverted cone, is filled with water to the brim. Its height is 20 cm and diameter is 16.8 cm. Two equal solid cones are dropped in it so that they are fully submerged. As a result, one-third of the water in the original cone overflows. What is the volume of each of the solid cones submerged ?

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

Assertion: If there are no external forces, the center of mass of a double star moves like a free particle. Reason: If we go to the center of mass frame, then we find that the two stars are moving in a circle about the center of mass, which is at rest.

The coordinates of the center of mass of the following quarter circular arc are

Assertion: Center of mass and center of gravity of a body will coincide on moon. Reason: There is no gravity on moon.

The surface area of a solid metallic sphere is 616\ c m^2 . It is melted and recast into a cone of height 28 cm. Find the diameter of the base of the cone so formed (Use pi=22//7 )

Find the centre of mass of a uniform solid cone.