We are interested in plugging a hole in a leaking tank using a spherical plug that places itself automatically as shown in Figure P1.21. A variation of this type of plug has been used for a long time to seal leaks in car radiators. A sphere of radius, $r_{o}$, and specific gravity, s.g., is submerged in a tank of water. The sphere is placed over a hole of radius, $r_{i}$, in the bottom of the tank. Find an expression for the range of sphere specific gravities such that the sphere will remain on the bottom.

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FIGURE P1.21 H P air air Fbuoy grav