Question 1:
http://i.imgur.com/ARVLw9b.jpg
I'm fairly certain it is correct. But the general idea is to determine the sum of moments about a point where you don't need to calculate some unknown values (in this case, it would be B
x and B
y.
As for Question 9, I haven't done that in a while, so I'm a bit sketchy on what you need to do. However, just from observation, the number of revolutions must be a function of the number of teeth, otherwise there not be any benefit from adding or removing teeth. From intuition, the answer must be 49/17.
Edit: I misread the angle in question 1 - should have been 60 degrees not 50 degrees.