6) A sphere of radius R, made from a material of specific gravity SG, is submerged in a tank of water. The sphere is placed over a hole of radius a in the tank bottom open to the atmosphere, as shown in the diagram below. Assume a is much smaller than R.

a) Develop a general equation for the range of specific gravities for which the sphere will float to the surface.

b) For the values given, determine the minimum SG required for the sphere to remain in the position shown.