With out inertia, how would an object that is experiencing a centripetal force behave?

The body will move towards the center.

Explanation:

When the object moves in a circle, the centripetal force is applied towards the center.

Due to inertia of motion, equal and opposite force is developed, acting outwards from center of circle.

This force is called centrifugal force, which balances the centripetal force and the body remains in a circle.

If there is no inertia, this outward force will be zero. thus the body will move towards the center due to its one force called centripetal force.