Determine the centre of mass of a uniform hemisphere of radius R.

Explanation

To determine the center of mass of a uniform hemisphere of radius \( R \), we can follow these steps:

### Step 1: Define the Geometry
We have a uniform hemisphere with radius \( R \). We can set up a coordinate system where the flat circular face of the hemisphere lies on the xy-plane, and the curved surface extends upwards along the z-axis. The center of the flat face is at the origin (0, 0, 0).

### Step 2: Consider a Differential Element
To find the center of mass, we will consider a differential mass element. We can take a thin semicircular ring at a distance \( r \) from the center of the flat face, with a small thickness \( dr \).

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