Newton's Second Law question, 3 blocks acting to each other

[The Lich King]

Homework Statement

Initially, the system of objects shown in figure is held motionless, the pulley and all surfaces and wheels are frictionless. Let the force F be zero and assume that m1 can move only vertically.

https://drive.google.com/file/d/0B6xlSNQyGbU5M3FTSXpNSVdmT2c/view?usp=sharing

2. Homework Equations
At the instant after the system of objects is released, find (a) the tension T in the string. (b) the acceleration of m2, (c) the acceleration of M, and (d) the acceleration of m1.

The Attempt at a Solution

For this problem I figured it out first based on the solution from Chegg. The key was to use the relationship between the accelerations of M and m2. I think by using the tension force divide by m2 can find out the acceleration of m2 with respect to the block M at the beginning. However after I asked my professor about this problem, he told me that by using the net force exerting on an object divide by its mass can always find out the its acceleration with respect to the ground. But in this way I could not figure out how to solve this problem again. I think if what my professor had said was right then by using the force exerting on m2, I can find out the acceleration of m2 with respect to the ground very easily then I can write (m1g-T)/m1=T/m2 which will give me a wrong answer. I am confused about this problem. Please tell me what is wrong and if I misunderstood what my professor had said. Thank you.

 

[Simon Bridge]

Since you have already solved the problem using relative motion, you can use the relationship to derive the equation entirely in terms of the ground-frame, to give you an insight into what your prof was saying.