Final answer:
The centripetal force acting on Marble A is four times greater than that of Marble B because centripetal force is proportional to the square of the velocity, and Marble A is moving at twice the speed of Marble B.
Step-by-step explanation:
The question deals with centripetal force, which is the force required to keep an object moving in a circular path and is directed towards the center of the circle. According to Newton's second law, the centripetal force (F) can be calculated using the mass (m) of the object, the velocity (v) at which it is moving, and the radius (r) of the circular path, with the formula F = m × v^2 ÷ r.
The mass of the marbles isn't provided, but we can compare the forces in terms of the ratio of their velocities since the masses are the same and the radius of the circular track would be constant for both marbles.
If Marble B has a centripetal force F when moving at 6 m/s, then Marble A, moving at twice that speed (12 m/s), will experience four times the centripetal force of Marble B, because centripetal force is proportional to the square of the velocity. Therefore, if the centripetal force acting on Marble B is F, the centripetal force acting on Marble A would be 4F.