From a uniform circular disc of radius `R`, a circular disc of radius `R//6` and having centre at a distance `R//2` from the centre of the disc is removed. Determine the centre of mass of remaining portion of the disc.

Explanation

To determine the center of mass of the remaining portion of the disc after removing a smaller disc, we can follow these steps:

### Step 1: Define the Problem
We have a uniform circular disc of radius \( R \) and we are removing a smaller disc of radius \( \frac{R}{6} \) which is located at a distance \( \frac{R}{2} \) from the center of the larger disc.

### Step 2: Calculate the Masses
1. **Mass of the larger disc (M1)**:
The area of the larger disc is \( A_1 = \pi R^2 \). Assuming uniform density \( \sigma \) (mass per unit area), the mass \( M_1 \) is given by:
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