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 solve the problem, we need to find the distance of the center of mass of the remaining part of the disc after removing a smaller disc. Here’s a step-by-step solution:

### Step 1: Understand the Geometry
We have a large disc of radius \( R \) and mass \( M \). A smaller disc of radius \( \frac{R}{2} \) is removed from it. The center of the smaller disc is located at a distance \( R \) from the center of the larger disc along the radius.

### Step 2: Calculate the Mass of the Smaller Disc
The mass of the smaller disc can be calculated using the area ratio since both discs are uniform. The area of the larger disc is \( \pi R^2 \) and the area of the smaller disc is \( \pi \left(\frac{R}{2}\right)^2 = \frac{\pi R^2}{4} \).

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