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An air bubble doubles in radius on risin...

An air bubble doubles in radius on rising from bottom of a lake to its surface. If the atmosphere pressure is equal to that due ot a column of `10` m of water, then what will be the depth of the lake.
(Assuming that surface tension is negligible)?

Text Solution

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Given that constant temperature , we use `P_(1)V_(1) = P_(2) V_(2)`
`P_(2) = (10)` dg (for water column) ` P_(1) = (10+h)` dg (where h=depth of lake)
` V_(1) = (4pi)/(3) r^(3) , V_(2)= (4pi)/(3) (2r)^(3) = 8((4pi)/(3) r^(3)) = 8V_(1)` Thus for `P_(2)V_(2) = P_(1)V_(1)`,
We have `10` dg `(8V_(1))= (10+h)` dg `V_(1) implies 80= 10+h implies h=70m`
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