A solid cylinder having radius R and mass M begins from rest and rolls devoid of slipping down an incline forming an angle of with horizontal. If the cylinder gets to the bottom of ramp, its center of mass has dropped a vertical distance h. Suppose, g represents the gravitational constant. The coefficient of static friction among the cylinder and the surface is µ s.
i) Determine the minimum value for the coefficient of static friction µ s in such a way that the cylinder rolls without slipping down the incline plane? Represent your answer in terms of M, R, g, and h as required.
ii) Determine the magnitude of the velocity of the center of mass of the cylinder if it reaches the bottom of the incline? Represent your answer in terms of M, R, g, and h as required.