Calculating Velocity for Energy Conservation in Rotating System

[Tiba]

Homework Statement

In the image below, there are two balls of mass m attached to a massless rigid metal steam, which can rotate around the point A. Give the necessary velocity to be applied in the lowest ball for the system to reach the horizontal line. Do not consider any system's energy loss.

Homework Equations

The Attempt at a Solution

I considered the center of the mass to be between the balls and established the following relationship:

mv²/2 + mgj/2 = 2mgj
v² = 3gj

This being the velocity of the center of mass.
However, the velocity of the center of mass is 3/4 of the velocity of the lowest ball (Vb), since the radius of center of mass is 3/4 the radius of the lowest ball.
v = 3/4*Vb
3gj = 9/16*Vb²
Vb = sqrt(16/3*gj)

Which is wrong.
Can someone please tell me what I'm doing wrong?
Thanks!

 

[voko]

Why do you care about the center of mass? You just need the potential energies of the balls in the horizontal position, and the kinetic energies in the vertical position. The kinetic energies are related to each other because the balls' velocities are related.

 

[CWatters]

What he said. Work out the change in PE required. The system must have at least that much KE at the bottom.