1' Consider a sphere of radius R, = .25m and mass M = 2kg (uniformly distributed) placed at the top of a ramp inclined at an angle I9 = 30: The center of mass of the sphere is a height h = 4m above the oor (throughout this problem the term \"floor\" refers to the at, horizontal region to the right of the ramp}. The sphere is released from rest. a.) If there is no friction what is the speed of the center of mass of the sphere when it reaches the oor? b) Now suppose there is friction, but the sphere rolls without slipping. What is the speed of the center of mass of the sphere when it reaches the oor in this case? How does it compared to part a)? c) What is the minimum coefcient of static friction such that rolling without slipping is possible when the sphere travels down the ramp? (1) Now suppose the sphere is hollow: all of the mass is located a distance R from the center of the sphere (the total mass M and the radius R are the same as before though). The moment of inertia. of a hollow sphere rotating around an axis through its center is I : TEMRZ. If we placed this sphere at the top of the ramp (at the same height as part a) and again it is released from rest) what is the speed of its center of mass when it reaches the floor for the case with friction and the case without friction? For the case with friction you may again assume the sphere rolls without slipping. How do your answers compare to parts a) and b)? e) In general if there is friction what is the eect of a larger moment of inertia on the speed of the center of mass when an object rolls downhill without slipping