Question

From a circular disc of radius \( R \), a square is cut out with a radius as its diagonal. The centre of mass of the remaining portion is at a distance (from the centre)

• A. \( \frac{R}{4\pi - 2} \)
• B. \( \frac{R}{2\pi} \)
• C. \( \frac{R}{\pi - 2} \)
• D. \( \frac{R}{2\pi - 2} \)

Hint:

For composite bodies, find the center of mass by subtracting the center of mass of the removed portion from the whole body.

Answer 1

The Correct Option is A

To solve this, we need to calculate the center of mass of the remaining portion after cutting the square out of the circular disc. First, calculate the area of the square and find its center of mass. Then, by subtracting the area of the square from the disc, we can calculate the new center of mass of the remaining portion. The center of mass of the remaining portion will be at a distance \( \frac{R}{4\pi - 2} \) from the center of the original disc. Thus, the correct answer is (A).