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If you just set the object in the water, the buoyant force never becomes greater than the object's weight.

It sinks and sinks, displacing more and more water, building up more and more buoyant force, until the

buoyant force is equal to its weight. At that point, the net force on it is zero, it stops sinking, and it stays

right there (floating).

The only way you can produce a buoyant force greater than its weight is to force it further down and hold it there.

Since the buoyant force is greater than its weight, as soon as you let go, the net force on it is up, and it'll rise,

partly out of the water until the buoyant force drops to equal its weight, and again ... it'll stay right there.

So the answer to the question is: An object can't stay indefinitely in a position where the buoyant force

is greater than its weight. If that happens, then it lifts some of itself out of the water, reducing the

buoyant force, until the buoyant force is again just equal to its weight.

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