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Question

# When an air bubble of radius r rises from the bottom to the surface of a lake, its radius becomes 5r4. Taking the atmospheric pressure to be equal to 10m height of water column, the depth of the lake would approximately be (ignore the surface tension and the effect of temperature):

A
10.5m
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B
8.7m
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C
11.2m
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D
9.5m
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Solution

## The correct option is D 9.5mPressure at bottom (P1)=Patm+ρgh+4TR1__________(1)Pressure at top(P2)=Patm+4TR2____________(2)Given R1=rR2=5r4So P1V1=P2V2(P1)43πr3=(P2)43125r364Dividing (1) and (2)P1P2=Patm+ρgh+4TrPatm+4T×45r=12564ρg(10)+ρghρg(10)=12564640+64h=1250On solving we get h=9.5m

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