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.

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

2.The hollow sphere will reach the bottom before the solid sphere.

Explanation / Answer

Rotational KE = 0.5 IW^2

where I is moment of inertia = c Mr^2

where c is constant and is different for different bodies

for solid homogeneous sphere c = 2/5

thin spherical shell, c = 2/3

a solid homogeneous cylinder c = 1/2

and a hoop = 1/2

so for larger C, larger Rot KE

so

part A : false

part B : False ,

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