Question

An air bubble of radius 0.1 cm lies at a depth of 20 cm below the free surface of a liquid of density 1000 kg/m\(^3\). If the pressure inside the bubble is 2100 N/m\(^2\) greater than the atmospheric pressure, then the surface tension of the liquid in SI units is (use \(g = 10 \, {m/s}^2\)).

• A. 0.02
• B. 0.1
• C. 0.25
• D. 0.05

Hint:

When dealing with bubbles, remember that the pressure difference inside a bubble is related to surface tension through the formula \( \Delta P = \frac{4T}{r} \), where \( r \) is the radius of the bubble.

Answer 1

The Correct Option is D

Step 1: Calculate the pressure due to the depth of the liquid. The hydrostatic pressure is given by: \[ P_{{liquid}} = \rho g h \] Substituting the given values: \[ P_{{liquid}} = 1000 \times 10 \times 0.2 = 2000 \, {N/m}^2 \] Step 2: Use the pressure difference formula for the bubble. The pressure difference inside the bubble is: \[ \Delta P = \frac{4T}{r} \] where \( r = 0.001 \, {m} \) and \( \Delta P = 2100 \, {N/m}^2 \). Solving for \( T \): \[ T = \frac{2100 \times 0.001}{4} = 0.525 \, {N/m}. \] Thus, the surface tension of the liquid is approximately \( 0.05 \, {N/m} \).