Distance of the centre of mass of a solid uniform cone from its vertex is z 0 . If the radius of its base is R and its height is h then z 0 is equal to:

Step-by-step solution

Let the mass of solid cylinder is M and angle with vertical is θ . Now, we take a small element of thickness d y at a distance y from the vertex. The radius of small element is r , as shown in the figure below. Then, tanθ = R h = r y which will give, r = y tanθ . The density of the cone is given by, ρ = M 1 3 π R 2 h = 3 M π R 2 h . The mass of the small element is given by, d M = ρ d V d M = 3 M π R 2 h × π r 2 d y = 3 M y 2 tan 2 θ R 2 h d y The center of mas