If a hoop and a cylinder of the same mass and radius are realeased from rest...

If a hoop and a cylinder of the same mass and radius are realeased from rest at the top of an incline at the same time, which one will reach the bottom first?

Expert Solution

The cylinder will reach the bottom first.

The rolling of object without slipping acceleration depends upon gravity , angle of inclination and moment of inertia of the object.and since acceleration due to gravity and angle of inclined plane is same for both the object so, only thing the motion of the object depends upon is the moment of inertia.

and we know that moment of inertia is nothing but the resistance offered to the rotational motion of the object.

so finally the object with the least moment of inertia between the two,( cylinder and loop) would reach the bottom of the inclined plane first than the other with greater moment of inertia. also the mass and radius are same for both the object then we need to consider overall value of moment of inertia itself.

moreover,

moment of inertia of a cylinder = 1/2 MR²

moment of inertia of a hoop = MR²

so, cylinder has a least value M.I so it will reach the bottom of the inclined plane first.

genius_generous answered 2 years ago

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