It is shown in the theory of gravitational attraction that a wire bent in the form of a circle of radius a exerts a force, f , upon a particle in the axis of the circle (i.e., in the line through the centre of the circle perpendicular to the plane of the circle), where f (h) ∝ h

(a 2 + h 2

)

3/2

, where h is the height of the particle above the plane of the circle.

a. What is the force when h = 0? Why?

b. What is the limit of the force as h → ∞? Why?

c. Is there a value of h that gives a maximal gravitational force on the object? Answer this without doing any math calculations.

You don’t have to find the value of h, just determine whether or not one exists.

d. What value of h gives the maximal gravitational force on the object?