Posted by Alex on Monday, January 9, 2012 at 10:57pm.
I will assume that the axis of the wedge is vertically upward. The force on the ball at each contact point is directed toward the center of the sphere at each contact point, because there is no friction. The contact force angle is inclined (180-110)/2 = 35 degrees to the horizontal. A vertical force balance tells you that the two contact forces F are equal in magnitude (due to symmetry) and that
2F sin35 = 2F cos55 = M g
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