Question

Find the position of the center of mass of a hollow hemisphere of radius $R=10\text{cm}$. Assume center $\text{O}$ as origin.

• A. $(0,10)\text{cm}$
• B. $(0,2.5)\text{cm}$
• C. $(0,5)\text{cm}$
• D. $(0,0)\text{cm}$

Answer 1

The correct option is C $(0,5)\text{cm}$


Given radius $R=10\text{cm.}$
Hollow hemisphere is symmetric about $y-$ axis. So, the $x-$ co-ordinate of $COM$ of hemisphere is zero.
$\Rightarrow x_{COM}=0$

We know, the height of $COM$ of hollow hemisphere from its geometric center $\text{O}=\frac{R}{2}$
i.e $y_{COM}=\frac{10}{2}=5\text{cm.}$
So, position of COM of hollow hemisphere is
$(x_{COM},y_{COM})=(0,5\text{cm})$