A sphere of mass M is attached to one end of a rigid stick of negligible mass. The other end of the stick is fixed in place so that the sphere can move in a circular path of radius R (a) The sphere is released from rest with the stick at an angle of 60 degrees from the vertical, as shown in Figure 2. Derive an expression for the speed of the sphere when it is at point B, the bottommost point of the circular path.

(b) An external force is exerted on the sphere to speed it up. After the force is removed, the sphere has enough speed to move in a complete circle, as shown in Figure 3. The angle θ is equal to zero when the sphere is at point B and is 180 degrees when the sphere is at point T, the topmost point of the circular path.

(c) When the sphere makes a complete revolution around its circular path, does it spend more time in the top half of the circle, more time in the bottom half of the circle, or the same amount of time in both halves of the circle? Briefly state your reasoning.