Question

A. large bubble rising from the bottom. of a lake to its surface gets its radius doubled. if the atmospheric pressure is equal to the water column of height h, what is the depth of lake?



a.h



b.2h



c.7h



d.sh.

Answer 1

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✔ option (c)
The radius doubling implies that the volume has become eight times it's original volume(at the bottom) when it is at the top of the lake.

Now assuming the air to follow ideal gas behaviour we can write PV=K or pressure is inversely proportional to volume.

So since the volume increases eight times from bottom to top of the lake, pressure at the bottom has to be eight times more than what it is at the top of the lake.

Since the atmospheric pressure corresponds to a water level H,the depth of the lake would be 7 times H.

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