Final answer:
If the centripetal force acting on an object in uniform circular motion were removed, the object would travel in the direction of its tangential velocity at the moment the force was removed, according to Newton's first law of motion. option c. in the direction of the tangential velocity is the correct answer.
Step-by-step explanation:
When discussing uniform circular motion, the concept of centripetal force is pivotal. An object in constant circular motion is consistently being pulled towards the center of its circular path by this centripetal force, resulting in a change of direction that constitutes acceleration towards the center, known as centripetal acceleration. Newton's second law tells us that the net force on an object is equal to its mass times its acceleration (net F = ma), and in the case of uniform circular motion, this force is the centripetal force (Fc).
Now, if we suppose the centripetal force was removed, the object would no longer be pulled toward the center. According to Newton's first law of motion, an object in motion will stay in motion with the same speed and in the same direction unless acted upon by an unbalanced force. Since the centripetal force was providing the necessary centripetal acceleration for keeping the object in circular motion, once it is removed, the object would no longer accelerate toward the center. Consequently, the object would continue moving in the direction of its tangential velocity at the point where the force was removed.
Therefore, the correct option is (c) in the direction of the tangential velocity, as this is the direction an object naturally takes due to its inertia when it is no longer subject to the centripetal force.