An object would in the absence of a force continue to move in a straight line. If an object has to move in a circular path a force is required to pull it towards the center and make it move in a circular path rather than a straight line.

For an object with mass m moving with a velocity v, the force required to make it move in a circular path with radius r is m*v^2/r.

Here, as the two objects are identical they have an equal mass. One of them is moving at a speed that is twice that of the other. Let the speed of the slower object be v. The centripetal force required to keep it moving in a circular path is m*v^2/r. The centripetal force required to keep the faster object moving in a circular path is m*(2v)^2/r = 4*m*v^2/r.

This gives the correct answer as option 1. The centripetal force required to keep the faster object on the circular path is four times as much as the force required to keep the slower object on the path.

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