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Sd32.A bubble of gas released at the bottom of a lake increasesto four times its original volume when it reaches the surface.Assuming that atmospheric pressure is equivalent to thepressure exerted by a column of water 10 m high, what isthe depth of the lake(a) 20m (b) 10m (c) 30m (d) 40m |
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Answer» Let the pressure at the bottom =P1and volume =V1Let the pressure at the surface =P2and volume = V2Temperature remains constant soP1V1= P2V2Given that: V2= 4V1therefore, P1= 4P2 Pressure =hρgρ= density of waterg = acceleration due to gravity P2=hρg=10ρgP1= 4(10ρg) P1-P2=40ρg-10ρg=30ρg From hydrostatics,P1-P2=hρg30ρg =hρgh = 30 m Depth of the lake = 30m |
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