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A rigid sphere of radius $R_S$ made from a material with specific gravity $SG_s$ is completely submerged in a tank of water with radius $R_t$ and initial depth $L$ as shown in the figure

enter image description here The sphere is placed over a small hole of radius a in the bottom of the tank that is open to the atmosphere.

Find an inequality were the sphere will remain sitting on the bottom of the tank plugging the hole. You may assume that $a<< R_S$

How do I begin to solve this? Can someone point me in the right direction?

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Please give what you have tried . It will help us to help you and skip what all you know. – ABC Apr 25 '13 at 9:54
I dont know how to start solving it... – Ven Apr 25 '13 at 9:59
Suppose instead of a sphere you had a disk (of neutral bouyancy) covering the hole. What would the net force on the disk be? – John Rennie Apr 25 '13 at 11:55
To put @JohnRennie's comment another way, suppose the hole is obstructed by a circular stopper, held there by the weight of water above the hole. Then assume the sphere is trying to float but is tethered to the stopper. You want to know how much bouyancy it needs to just barely lift the stopper. – Mike Dunlavey Apr 25 '13 at 19:00

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