Answer:
the child have to exert this much amount of force radially to stay on the wheel.
Explanation:
Given:
mass of the child, 
radius of the merry-go round wheel, 
moment of inertia of the wheel, 
angular velocity of the wheel, 
Since the child is sitting on the edge of the rotating wheel the child will feel and outward throwing force called centrifugal force.
Centrifugal force is mathematically given as:


the child have to exert this much amount of force radially to stay on the wheel.