Newton's Third Law/ Circular Motion

[dekoi]

Question:
Mass m1 on the frictionless table is connected by a string through a hole in the table to a hanging mass m2. With what speed must m1 rotate in a circle of radius r if m2 is to remain hanging at rest?

My answer:
Fnetym2 = T - m2g
For m2, a = 0
Therefore,
0 = T - m2g
T = m2g

Fnetxm1 = T
m1a = T
m1a = m2g
Therefore,
a = m2g / m1

Since a = v^2 / r, v = sqrt(ra)

Therefore,
v = sqrt(rm2g / m1)

Is this correct?

 

[Päällikkö]

Looks correct to me.