In the figure, four point masses are placed as shown (2.0 kg, 4.0 kg, M1, and M2).
 

Take M1 = 8.0 kg and M2 = 6.0 kg.

a) Find the  x and y coordinates of the center of mass (CM). Show your work.

b) Compute the moment of inertia of the four masses about the CM. Do so without using the parallel axis theorem. Show your work.

c) Compute the the moment of inertia of the four masses about point O. Do so without using the parallel axis theorem. Show your work.

d) Check that your computations in b and c are consistent with the parallel axis theorem.

y 2.0 m 3.0 m 3.0 m M 0 2.0 m 2.0 kg 2.0 m 4.0 kg 3.0 m M 3.0 m 2.0 m