Suppose if you whirl a yo-yo about your head in a horizontal circle. in what direction must a force act on the yoyo? What exerts the force?

Direction of force towards the center and string apply the force.

Explanation:

Lets take

Mass of yo-yo = m

Length of string = L

Angular speed = ω

The radial acceleration a = ω² L

Then the radial force on the yo yo given as

F = m ω² L

Then this radial force act towards the center of the circle formed by yo - yo. The force exerted by string.

So the direction of force towards the center and string apply the force.