Find the centre of mass of a uniform semicircular ring of radius `R` and mass `M`.

Explanation

To find the center of mass of a uniform semicircular ring of radius \( R \) and mass \( M \), we can follow these steps:

### Step 1: Define the Geometry
Consider a semicircular ring with radius \( R \). The center of the semicircle is at the origin (0, 0) in a Cartesian coordinate system. The semicircular ring extends from \( -R \) to \( R \) along the x-axis and is symmetric about the y-axis.

### Step 2: Set Up the Differential Mass Element
Since the ring is uniform, we can define the mass per unit length \( \lambda \):
\[
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