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

Answer

B

Explanation

Mass of elementary disc,
`dm = pir^(2)` dze

`r/R = z/h rArr r =(Rz)/h`
`Z_(0) =(int zdm)/(int dm) =(int_(0)^(h) pi r^(2) dzez)/(1/3 pi R^(2) he) = 3/4 h`