Auniform thin wire is bent into a quarter-circle of radius a = 20.0 cm, and placed in the first quadrant. determine the coordinates of its center of mass with respect to the origin of coordinates at the center of the "full" circle.

Explanation:

The general equation to calculate the center of mass is:

Any differential of mass can be calculated as:

 Where "a" is the radius of the circle and λ is the linear density of the wire.

The linear density is given by:

So, the differential of mass is:

Now we proceed to calculate X and Y coordinates of the center of mass separately:

Solving both integrals, we get:

Therefore, the position of the center of mass is:

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