Consider a circular disc of radius 20 cm with centre located at the origin. A circular hole of radius 5 cm is cut from this disc in such a way that the edge of the hole touches the edge of the disc. The distance of centre of mass of residual or remaining disc from the origin will be

Solution

Physics sir · 3 steps

Treat the hole as a negative mass sitting at its own centre. Then it is a two-body centre of mass problem.

1. Locate the hole. The hole touches the rim from the inside, so its centre is 20 - 5 = 15 cm from the origin. Put it on the x-axis at x = 15 cm.
2. Mass goes as area. For a uniform disc, mass is proportional to r². Take the full disc as 20² = 400 units at x = 0. The removed part is 5² = 25 units at x = 15. The remaining disc is 400 - 25 = 375 units.

   x_(cm) = (400 × 0 - 25 × 15)/(400 - 25) = -375/375 = -1 cm

3. So. The centre of mass of the remaining disc is 1 cm from the origin, on the side opposite the hole. The answer is (d) 1.0 cm.

The idea to keep. For a body with a piece cut out, subtract the piece as a negative mass placed at its own centre. The centre of mass always shifts away from the hole.

Answer from the NTA final answer key. Solution by PrepWiser.