A box of length 
and weight 
is placed on a horizontal table, with the greater part of its length overhanging the edge of the table. The edge of the table acts as a pivot. The centre of gravity of the box is at its geometric centre. To balance the box, a uniform sphere of diameter 
is placed inside the box, touching one end, as shown.
Assume that the forces acting on the box are in the plane of the diagram. What is the minimum mass of the sphere that is needed to maintain the system in equilibrium?
