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![[Post New]](/templates/default/images/icon_minipost_new.gif) 1 Feb 2008 11:27:15 IST
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An expansible balloon filled with air floats on the surface of the
lake with 2/3rd of its volume submerged.How deep must it be
sunk in the water so that it is just in equilibrium neither sinking
further nor rising? It is assumed that the temperature of the
water is constant and that the height of the water barometer is
9meters.
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"Nenenthedhavano naake teleedu"
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1 Feb 2008 19:41:56 IST
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Do you think there is some mistake in the question itself  ?
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1 Feb 2008 19:45:53 IST
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yeah i agree with u...
if it floats at 2V/3 then t is already at equilibrium
so what do we find?
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1 Feb 2008 19:48:03 IST
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no d question is right as when it is submerged a little outer pressure will increse an the volume of the baloon will decrease. hence to balance the wieght more volume of water will hv to be diisplaced
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1 Feb 2008 21:15:13 IST
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The question is correct. Its beautifully framed.
The height of the barometer gives you the atmospheric pressure at the location where the experiment is carried out.
The initial equilibrium of 2/3rd floating gives you the density of the balloon at that time.
Let it be submerged to a depth h below the water. You can find the pressure there in terms of h. Next using Boyle's law find the relation between the density of the balloon at depth h. Use the condition for equilibrium. You should get h
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1 Feb 2008 21:53:39 IST
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Sir can u plz explain the sentence "Let it be submerged to a depth h below the water. You can find the pressure there in terms of h. Next using Boyle's law find the relation between the density of the balloon at depth h." more clearly?....just explain it sir ,..i'll do the calculation .
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1 Feb 2008 23:28:10 IST
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Harsha,
As the balloon is expansible, V will change. But it is given that T is constant. So, it is isothermal change. So, PV is constant.
Let P' be the atmospheric pressure there. This will be found by the fact that height of water barometer is 9m.
1 atm atmospheric pressure = 13.6 m height of water barometer.
So, 9m height = 9/13.6 atm = P'
Hopefully you will be able to calculate it now.
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