Some curious students hold a rolling race by rolling four items down a steep hil

Question

Some curious students hold a rolling race by rolling four items down a steep hill. The four items are a solid homogeneous sphere, a thin spherical shell, a solid homogeneous cylinder and a hoop with all its mass concentrated on the hoop's perimeter. All of the objects have the same mass and start from rest. Assume that the objects roll without slipping and that air resistance and rolling resistance are negligible. For each statement below, select True or False.

The homogeneous sphere finishes first.

Upon reaching the bottom of the hill, the homogeneous sphere will have a smaller rotational kinetic energy than any of the other objects will when they reach the bottom of the hill.

Explanation / Answer

true

it velocity is more than others

vf sphere = sqrt(10/7*gh)

vf spherical shell = sqrt(6/5* gh)

vf hoop = sqrt(gh)

vf cylinder = sqrt(4/3*gh)

sphere has more velocity than others it will reach first at bottom

false

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