Question

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 heights is h, then $Z_0$ is equal to ?

• A. $\frac{3h}{4}$
• B. $\frac{h^2}{4R}$
• C. $\frac{5h}{8}$
• D. $\frac{3h^2}{8R}$

Answer 1

The correct option is A

$\frac{3h}{4}$

Consider an elementary disc of the cone of thickness dz at a distance z from the vertex.

Mass of the disc = $\rho \pi (ztan\theta {)}^{2}dz$ where $\rho$ is volume mass density.
Now, centre of mass, $Z_{CM}=\frac{{\int }_0^{h}zdm}{{\int }_0^{h}dm}=\frac{3h}{4}$