Find coordinates of mass center of a quarter ring of radius r placed in the first quadrant of a Cartesian coordinate system, with centre at origin.

Explanation

To find the coordinates of the center of mass of a quarter ring of radius \( r \) placed in the first quadrant of a Cartesian coordinate system with the center at the origin, we can follow these steps:

### Step 1: Understand the Geometry
The quarter ring is a circular arc that spans an angle of \( \frac{\pi}{2} \) radians (or 90 degrees) and is located in the first quadrant. The center of the quarter ring is at the origin (0, 0).

### Step 2: Determine the Angle
For a quarter ring, the angle subtended at the center is \( \frac{\pi}{2} \). Therefore, the angle \( \theta \) we will use in our calculations is \( \frac{\pi}{4} \) because the angle \( 2\theta \) is equal to \( \frac{\pi}{2} \).

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