The tangential velocity is proportional to the length of the rope hence when the length of the rope is doubled, the tangential velocity becomes two times greater.
We know that the tangential velocity of an object moving along a circular path depends on its radius and it's angular velocity.
In this case, we have been told that the motion of the object is uniform meaning that the angular velocity is held constant and the length of the rope which is the radius was doubled.
Since the tangential velocity is directly proportional to the length of the rope, the tangential velocity will be two times greater when the length of the rope is doubled.
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