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1. From Archimedeus Principle, upthruse=weight of fluid displaced

Let dh and da be the densities of hydrogen and air respectively
V be the volume of the balloon.

Hence, weight of balloon = (V.dh).g where g is the acceleration due to gravity
The volume of air displaced = V
thus, upthrust = (V.da).g

Since da is greater than dh,
(V.dh).g is smaller than (V.da).g
i.e. weight of balloon is smaller than upthrust
there is a net upward force which makes the balloon to move up.
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2. From the same principle, upthrust acting on a swimmer
= (V.dw).g
where V is the volume of the swimmer and dw is the density of sea water

For a swimmer to float, (V.dw)g must be, at least, equal to the weight of the swimmer .

i.e. (V.dw)g = mg where m is the mass of the swimmer

In the dead sea, the water density is much higher than ordinary sea water because of the abundance of dissolved salt in it.

Thus, the increase of dw will make the term (V.dw)g be greater than mg (weight of the swimmer). The swimmer will always float.

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http://hk.knowledge.yahoo.com/question/?qid=7006111602345
Almost the same