The correct answer is A) The barge may pass under the hawser and capsize the tug. When attempting to swing a barge on a hawser to slow its speed, the principal danger is that the barge may swing too far and pass under the hawser, potentially capsizing the tug. This can happen if the barge swings too quickly or the turn is too tight, allowing the barge to pass under the hawser and destabilize the tug. The other options are incorrect because: B) The barge swinging too quickly is not the primary danger, but a symptom of the principal issue. C) Dangerous wakes are a secondary concern, not the main risk. D) Free surface effect is not the main factor in this scenario.