From a uniform disc of radius `R`, a circular section of radius `R//2` is cut out. The centre of the hole is at `R//2` from the centre of the original disc. Locate the centre of mass of the resulating flat body.

Explanation

To find the center of mass of the resulting flat body after cutting out a circular section from a uniform disc, we can follow these steps:

### Step 1: Understand the Configuration
We have a uniform disc of radius \( R \) and we cut out a smaller disc of radius \( \frac{R}{2} \) from it. The center of the smaller disc is located at a distance \( \frac{R}{2} \) from the center of the original disc.

### Step 2: Define the Masses
Let the mass of the original disc be \( m \). Since the disc is uniform, the mass per unit area \( \sigma \) is constant. The area of the original disc is \( A = \pi R^2 \), so we can express the mass as:
\[
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