HELP PLEASE! A rigid massless rod is rotated about one end in a horizontal circle..?

Question

A rigid massless rod is rotated about one end in a horizontal circle
There is a mass m1 attached to the center of the rod and a mass m2 attached to the outer end of the rod. The inner section of the rod sustains three times as much tension as the outer section. Find the ratio m2/m1

The actual answer is .250 How you get to it....beats me....

Answer 1

The basic formula that we know in circular motion is:

F=mv^2/r,

where F is the centripetal force, m the mass, v is the linear velocity, and r is the radius.

We also know that v=wr

where v is the linear speed, w (supposed to be omega) is the angular velocity, and r is the radius.

Substitute the value of v in our first formula:

F=m(wr)^2/r
F =mw^2r Formula 1)

In this problem, we also know that w which is the angular velocity is the same for m1 as for m2 because they are located along the same line which is rotating about one end of the rod.

We are also given the value of the tension in the inner section as 3x that of the outer section. Let's draw a simple free body diagram:

T1=3F2<----0-->T2=F2<---0

The first 0 is m1 and the second 0 is m2.

The diagram might get distorted when I send it, but let's just cross our fingers it comes out clear enough.

The net force acting on m1 is (3F2-T2). But T2=F2.
Therefore, net force on m1 =3F2-F2=2F2. Let's call
this net force as F1. Thus F1=2F2. Now we also know
that

F1=m1w^2r
based on formula 1) above. Now substitute the value of F1=2F2, and we get:

2F2=m1w^2r Equation 1)

And based on the same formula F=mw^2r:

F2=m2w^2(2r) Equation 2)

Remember that for m2 the radius is twice that of m1, which is a given condition in this problem.

Now divide equation 2 by equation 1:

F2=m2w^2(2r)
------------------
2F2=m1w^2r

F2,w^2, and r will cancel out leaving:

1/2=2m2/m1

Divide both sides by 2:

1/4=m2/m1

m2/m1=1/4
=0.25

Answer 2

v = rω
F = mv²/r = mr²ω
F1 = m1r1²ω
F2 = m2r2²ω
m1r1²ω + m2r2²ω = 3m2r2²ω
m1r1² + m2r2² = 3m2r2²
m1r1² = 2m2r2²
r2 = 2r1
m1r1² = 2m2(2r1)²
m1 = 8m2
m2/m1 = 1/8