Fluid MechanicsHard
Question
A soap bubble of radius R and surface tension T is formed in vacuum. It is slowly charged so that it slowly expands. It is stopped charging when the radius becomes 2R. Find the amount of charge given to the bubble.
Options
A.Q = 
B.Q = 
C.Q = 
D.None of these
Solution
we have initially Pin = 
......(1)
Now when extra charge is given, for equilibrium we have
P′in +
......(1)
Now we have P′in =
[isothermal change]
where vi- initial volume of bubble
vf- final volume of bubble
so, P′in =
so, (1) equation will give
so, σ2 =
so, σ = 
now charge Q = σ. 4π(2R2) = 4π.(4R2) = 
Q =
......(1)Now when extra charge is given, for equilibrium we have
P′in +
......(1)Now we have P′in =
[isothermal change]where vi- initial volume of bubble
vf- final volume of bubble
so, P′in =
so, (1) equation will give
so, σ2 =
so, σ = now charge Q = σ. 4π(2R2) = 4π.(4R2)
= Q =
Create a free account to view solution
View Solution FreeMore Fluid Mechanics Questions
Two water pipes P and Q having diameters 2 × 10-2 m and 4 × 10-2 m, respectively, are joined in series with th...In a capillary tube, water rises by 1.2 mm. The height of water that will rise in another capillary tube having half the...If in the above problem the sphere is slightly displaced vertically from its equilibrium position, the time period of th...A boat having a length of 3 metre and breadth 2 metre is floating on a lake. The boat sinks by one cm when a man gets on...A non uniform cylinder of mass m, length l and radius r is having its centre of mass at a distance l/4 from the centre a...