Final answer:
Considering the forces acting upon falling marbles, a larger marble with greater mass and cross-sectional area will reach a higher terminal velocity compared to a smaller marble, because it requires a larger drag force to balance out the gravitational force. Therefore, the correct option is a).
Step-by-step explanation:
When comparing the terminal velocities of two marbles of different sizes, it's important to consider the forces acting upon them as they fall through a fluid-like air. The terminal velocity is reached when the force of gravity is balanced by the drag force; no further acceleration occurs, and the object falls at a constant speed. For spherical objects like marbles, the drag force is influenced by the cross-sectional area (which increases with the size of the marble) and the drag coefficient, which is similar for spheres of different sizes.
Terminal velocity is primarily determined by the balance between gravitational force, which depends on the mass (and therefore size) of the marble, and the drag force, which depends on the shape and cross-sectional area of the marble. Since larger marbles have greater mass, they require a larger drag force to balance the gravitational force. This means that a larger marble will typically reach a higher terminal velocity before the forces are in balance. Therefore, if two marbles of different sizes are taken, we would expect to observe that the larger marble has a higher terminal velocity than the smaller marble, given that all other conditions are equal. If we refer to the options provided initially, the correct option in the final part of the question would be: a) Larger marble has higher terminal velocity.