Object A is a uniform solid sphere of
mass M. Object B is a hollow sphere of the same mass M which is concentrated in
a uniform narrow strip at the surface of the sphere. The two objects have the
same radius R = 0.50 m. (Their densities are different.)

(a)
Starting from rest they are allowed to roll without slipping or sliding down a
hill that is 45 m above the
ground. What are their speeds at the bottom of the hill?

Show
all your work and explain why they are different if they are different or why
they are the same if they are the same.

(b)
The same two objects are allowed to start from rest and go down the same hill which is now covered by a sheet of ice so that
the two objects slide without rolling down
the hill. What are their speeds at the bottom of the hill?

Show
all your work and explain why they are different if they are different or why
they are the same if they are the same.