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 semicircular ring
We consider a uniform semicircular ring of radius \( R \) lying in the xy-plane, with its center at the origin. The mass \( M \) is uniformly distributed along the ring.

### Step 2: Set up the linear mass density
The linear mass density \( \lambda \) of the ring can be defined as:
\[
...