Problem Statement
A rigid massless rod is rotated about one end in a horizontal circle. There is a mass m_1 attached to the center of the rod and a mass m_2 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 m_2/m_1
Solution
Doing a force balance at both m_1 and m_2 shows that the centripetal force (F_c=m*v^2/r) will equal the tension. Though since their velocities will not be the same but their angular velocities will be I replaced velocity with radius*angular velocity.
F_c=m(rw)^2/r

For m_1...

Solve for T

For m_2...


Since T=T...

Solving for m_2/m_1 I get 2/3 but my book says the answer is 1/4.