In the planetary gear system shown, the radius of the central gear A is a = 20 mm, the radius of the planetary gear is b, and the radius of the outer gear E is (a + 2b). A clockwise couple of magnitude MA = 20 N ⋅ m is applied to the central gear A, and a counterclockwise couple of magnitude MS = 100 N ⋅ m is applied to the spider BCD. If the system is to be in equilibrium, determine 

(a) The required radius b of the planetary gears, 

(b) The couple ME that must be applied to the outer gear E.

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