How will the motion of the red marble placed at the edge of the flat sheet and given an initial velocity in the direction of the arrow compare with its motion on the curved sheet with a large mass in its center?

The marble will travel in a straight line on the flat sheet and in a line curving toward the central mass on the curved sheet.

Explanation:

This is a translational motion of a circular sphere

It has two motion,

1. Rotational motion: this occur at the curve edge.

2. Translational: this occur at the center and it moves on a straight line.

The motion at the edge is control by centripetal force.

Any force or combination of forces can cause a centripetal or radial acceleration.