An air bubble rises from the
bottom to the top of a lake. Its
volume (Assume temperature to
be constant)
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the volume of bubble must be constant
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When an air bubble rises from the bottom to the surface of a lake, its radius becomes double. The depth of the lake is d and the atmospheric pressure is equal to the pressure due to the column of water 10m high. Assume constant temperature and neglect the effect of surface tension and viscosity. Find the value of
10
d
Here the body force on the air bubble when it is at the bottom of the lake is equal to the body force on it when it is on the surface of the lake. i.e,
(P
0
+dρg)
3
4
πr
3
=P
0
3
4
π(2r)
3
Where P
0
=ρgh=10ρg= atmospheric pressure.
thus, (10ρg+dρg)=10ρg(8)
10+d=80⇒d=70
thus
10
d
=7
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