Step 1:

\

Point masses lying on $\"\"$ -axis are $\"\"$ and $\"\"$ .

\

$\"\"$ -axis points are $\"\"$ and $\"\"$ .

\

Center of mass is $\"\"$ and $\"\"$ .

\

where $\"\"$ is total mass of the system.

\

$\"\"$ The moment about $\"\"$ - axis $\"\"$ .

\

$\"\"$ The moment about $\"\"$ - axis $\"\"$ .

\

Here, we need to find center of mass about $\"\"$ -axis, so the $\"\"$ -coordinates are zeros.

\

Moment about $\"\"$ -axis $\"\"$ .

\

Step 2:

\

Total mass of the system is $\"\"$ .

\

Substitute $\"\"$ -axis points and point masses in $\"\"$ .

\

$\"\"$

\

Substitute $\"\"$ and $\"\"$ in center of mass formula.

\

$\"\"$

\

Center of mass $\"\"$

\

Solution:

\

Center of mass $\"\"$ .