Rolling Things
Classical Mechanics
Level
3
Two wooden wheels carry a 10-kilogram weight. One weight is a disk attached to the centre; the other is a ring attached near the rim. If the wheels are released simultaneously on an inclined plane, which will reach the bottom first?
Image credit: Wikipedia L. Mahin
The wheel with the weight near the rim will arrive first but it won't roll further than the other.
The wheel with the weight near the centre will arrive first and it will roll further than the other.
The wheel with the weight at the centre will arrive first but it wont roll further than the other.
The wheel with the weight at the centre will arrive first and it will roll further than the other.
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Mgh is converted to 1/2 m v square + 1/2 I w square.... The one which will reach first will be the one which has more velocity & since (1/2mv square + 1/2Iw square) is a constant... More velocity means lesser moment of inertia (MOI)... The one with lesser MOI is disc attached to the centre. Since it has lesser MOI it won't go much further....