Question

Find the co-ordinates of the center of mass of a hollow cone having a height of $90\text{cm}$ as shown in the figure.

• A. $(0,45)\text{cm}$
• B. $(0,60)\text{cm}$
• C. $(0,30)\text{cm}$
• D. $(0,25)\text{cm}$

Answer 1

The correct option is C $(0,30)\text{cm}$

Given height of the hollow cone $H=90\text{cm}$
$x-$co-ordinate of COM of the hollow cone is zero because the hollow cone is symmetric about $y-$ axis.
i.e $x_{COM}=0$

We know that, height of the COM of a hollow cone from the center of base of the cone is $\frac{H}{3}$
So, $y-$ co-ordinate of COM of the hollow cone,
$y_{COM}=\frac{H}{3}=\frac{90}{3}=30\text{cm}$
So, co-ordinates of $COM$ of the hollow cone are $(x_{COM},y_{COM})=(0,30)\text{cm}$