Answer:
Part a)

Part b)

Step-by-step explanation:
Part a)
Time period of one revolution is given as
T = 42 s
now the angular speed of the belt is given as



Now at rest position the force along the surface of carousel must be constant
so we will have



Part b)
New Time period of one revolution is given as
T = 30 s
now the angular speed of the belt is given as



Now at rest position the force along the surface of carousel must be constant
so we will have



Also we know that in perpendicular direction also force is balanced




now for friction coefficient we will have


