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A disc of radius R is cut out from a larger disc of radius 2R in such a way that the two circumferences touch each other. The centre of mass of the remaining lamina lies at a distance αR from the centre of the larger disc. What is the value of α?

1. 1/4
2. 1/3
3. 1/2
4. 1/6

Correct answer: 1/3

Solution

Mass scales with area: big disc (radius 2R) ~ 4m, removed disc (radius R) ~ m, with the small disc's center at distance R from the big center. COM = (4m.0 - m.R)/(4m - m) = -R/3, so the remaining lamina's COM is at R/3, i.e. alpha = 1/3.

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