immediately slew to the side that lost the track. (in your case to the right) How sharp the slew would depend on the speed of travel and/or if it were turning at the time of the track break (turning puts a lot of stress on the tracks and is probably the leading non-combat cause of a thrown/broken track).
With a front sprocketed tank, the sprocket would spin faster than the other track, literally pulling the track and throwing it out in front of the tank. The speed of travel at the time of the break would also determine the sharpness of the slew. The higher the speed the more unlikely the tank would be able to stop before the track was pulled through the sprocket and thrown out in front of the tank. The sprockets also put a great deal of stress on tracks, and, for example, if the track broke at the sprocket the first road-wheel would "dig in" to the ground and slew the tank to that side. If the track broke underneath the road wheels then the tank would act normally until the track tension is lost at the rear (idler) of the tank. When the tension is lost, the sprocket spins faster, pulling the loose track through and throwing it in front of the tank.
With a rear sprocketed tank the tracks would act similarly to the above, but the loss of tension would be at a different location.
As to the track behind the tank it would most likely be straight unless it had just made a turn when the track broke.
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