When the left ball is pulled to the side and then released, it will swing back towards its original position due to gravity. When it collides with the right ball, both balls will engage in a transfer of momentum due to the collision. Since both balls have the same mass, the effect of the collision will cause them to move in the direction of the swing.
In this scenario, the left ball will swing back and hit the right ball. Given the nature of the collision, both balls will swing to the right as a result of the left ball transferring its momentum to the right ball.
So, the correct answer is C: both balls will swing to the right.