Question

The total pressure \(P\) inside an air bubble of radius \(r\) at a depth \(h\) below the surface of liquid of density \(\rho\) is (T = surface tension of liquid, \(P_0\) = atmospheric pressure)

• A. \(P_0 - h\rho g - \frac{2T}{r}\)
• B. \(P_0 + h\rho g + \frac{2T}{r}\)
• C. \(P_0 + h\rho g + \frac{4T}{r}\)
• D. \(h\rho g + \frac{2T}{r}\)
• E. \(P_0 + \frac{2T}{r}\)

Hint:

For liquid bubble: excess pressure = \(2T/r\).

Answer 1

The Correct Option is B

Concept: Total pressure inside bubble:
• External pressure at depth = \(P_0 + h\rho g\)
• Excess pressure due to surface tension = \(\frac{2T}{r}\)

Step 1: Add pressures.
\[ P = P_0 + h\rho g + \frac{2T}{r} \]