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 :

Options

A. `(h^2)/(4R)`
B. `(3h)/(4)`
C. `(5h)/(8)`
D. `(3h^2)/(8R)`

Answer

B

Explanation

`dm = pir^2 dyrho`
`Y_(CM) = (intYdm)/(intdm) = (int_(0)^(h) pir^2 dy xx rho xx y)/(1/3 pi R^2 h rho) = (3h)/4 ("using" r/y = R/h)`