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Question

An air bubble doubles in radius on rising from bottom of a take to its surface. If the atmospheric pressure is equal to that due to a column of 10 m of water, then find the depth of the lake assume temperature constant and neglect surface tension -
  1. 20 m
  2. 50 m
  3. 70 m
  4. 40 m


Solution

The correct option is C 70 m
Assuming constant temperature, we useP1V1=P2V2Given:P2=(10)dg (for water column)P1=(10+h)dg(where h = depth of lake)V1=4π3r3V2=4π3(2r)3=8.(4π3r3)=8V1Thus for P2V2=P1V1, we have10dg(8V1)=(10+h)dgV1or 80=10+hh=70m
 

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