From a uniform circular disc of mass M and radius R a small circular disc of radius R/2 is removed in such a way that both have a common tangent. Find the distance of centre of mass of remaining part from the centre of original disc.

Explanation

To find the distance of the center of mass of the remaining part of the disc from the center of the original disc, we can follow these steps:

### Step 1: Understand the Problem
We have a uniform circular disc of mass \( M \) and radius \( R \). A smaller circular disc of radius \( \frac{R}{2} \) is removed from it such that both discs have a common tangent. We need to find the distance of the center of mass of the remaining part from the center of the original disc.

### Step 2: Determine the Mass of the Removed Disc
The mass of the original disc is given as \( M \). The area of the original disc is:
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