Suppose that the centripetal force acting on an object in circular motion were doubled to a new value, and the object remained in a circular path with the same radius. How would the motion be affected?

Centripetal force is mass times centripetal acceleration:

F = m v² / r

If force is doubled while mass and radius are held constant, then velocity will increase.

2F = m u² / r

2 m v² / r = m u² / r

2 v² = u²

u = v√2

So the velocity increases by a factor of √2.