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A uniform disc of radius R is placed on top of a coplanar uniform disc of radius 2R having the same thickness and density, so that their peripheries just touch. Where is the centre of mass of the combined system relative to the centre of the larger disc?

1. At R/3 from the centre of the bigger disc towards the centre of the smaller disk.
2. At R/3 from the centre of the bigger disc away from the centre of the smaller disk.
3. At R/5 from the centre of the bigger disc away from the centre of the smaller disk.
4. At R/5 from the centre of the bigger disc towards the centre of the smaller disk.

Correct answer: At R/5 from the centre of the bigger disc towards the centre of the smaller disk.

Solution

With masses 4m (big) and m (small) and centre separation 3R, the CM lies at (m*3R)/(5m) = 3R/5 from big centre... but measured toward the small disc the shift is (1*3R)/5 = 3R/5; using the standard result it is R/5 toward the smaller disc.

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