How to determine the mass of a galaxy? I am having a slight disagreement with my professor.

We can measure the mass of a distant star cluster from:
A.Its color
B.Its radius
C.Its metallicity
D.Smearing of lines in its total spectrum

My thinking was:
Law of Conservation of Energy

Kinetic Energy = Gravitational force

1/2*m*v^2 =  G* m*M/r

v = sqrt(2GM/r)

So it is dependant on both velocity and radius.
Answer choice D would give you the velocity but I responded with answer choice B, radius.
After talking it over with my professor, she responded with:

If we think about it conceptually, the dominant parameter is the velocity.  In other words, you can get a meaningful estimate of the cluster mass from the velocity dispersion without knowing the radius (because all clusters are the &quot;same&quot; size), but not vice versa.
So I'd say it still seems pretty clear that the best answer is the velocities.

Is she right or is the question worded poorly?
I think she should have clarified the question by putting velocity and radius in the same choice.

By looking at her answer, it seems reasonable to think that velocity is more important. However  without knowing the radius we cannot determine the mass of the stellar system. She argued this idea by saying that the size is approximately known for stellar systems. But I don't think that is a solid argument. 

Theoritically we should know both R and V to calculate M. 

Note: I did not understand why you wrote kinetic energy= gravitational force ? Thats not possible. 

In stellar bounded system you should use virial theorem. By stating that $-2&lt;E&gt;=&lt;U&gt;$  and from there you get 

$$M=v^2R/G$$