Ball revolving around a massive disc and a cube placed at centre

[someone_2156]

Homework Statement

Consider a thought experiment performed in free space. In the experiment, a small cube C of mass m is placed at the center of a large and highly massive disc D and a ball B of mass M revolves in circular path of radius R around the center of the disc. The plane of the circle is perpendicular to the plane of the disc as shown in the figure. Intensity of the gravitational field of the disc near its center is g. What should be range of coefficient of friction between the cube and the disc so that the cube remains motionless?

Relevant Equations

$F=GmM/R^2$

I thought that the maximum force on the block in the x direction would be the point where the ball crosses the plane of center and thus frictional force would be maximum, and if the block does not slip in that case then it never will slip as the value of force in x direction only decreases. However this gives a wrong solution. What is wrong with my line of thought in this problem?

 

[Steve4Physics]

Note that the normal reaction of the disc on the cube will change as the ball moves in its orbit. So the limiting frictional force will also depend on the position of the ball.

A free-body diagram of the cube with the ball at some arbitrary position should help.

Edit: And don't forget that the ball is sometimes below the disc's plane.