Answer
The track remains in equilibrium until the golf ball rolls off the track.
Work Step by Step
Suppose the billiard ball has 3 times the mass of the golf ball. The spring force is internal, so linear momentum is conserved. The billiard ball will roll to the right at one-third the speed of the golf ball.
At any time, the one-third-as-massive-golf ball is three times farther from the fulcrum than the billiard ball is. This means the golf ball's weight has a lever arm that is three times longer than the lever arm for the billiard ball.
The torques produced by the weights of the balls are equal and opposite, and the track balances. Once the faster-moving golf ball reaches the end and rolls off, the track tips clockwise.
