Question

Find the height (in cm) of the center of mass of a solid hemisphere of radius $R=8\text{cm}$ from geometric center of its base.

Answer 1

Let $\text{O}$ be the geometric center of the base of solid hemisphere. Take the origin at $\text{O}$ and coordinate axes are as shown in figure.


Then, the solid hemisphere is symmetric about $y-$ axis. So, $x-$ co-ordinate of $COM$ will be zero.
We know that, $y-$ co-ordinate of $COM$ of a solid hemisphere is at height $\frac{3R}{8}$ from its geometric center $\text{O}$.
So, height of $COM$ of the solid hemisphere of radius $R$ from its geometric center $\text{O}$
$=\frac{3R}{8}=\frac{3\times 8}{8}=3\text{cm}$