Question

A 0.02 cm liquid column balances the excess pressure inside a soap bubble of radius 7.5 mm. Determine the density of the liquid. Surface tension of soap solution = 0.03 N m^-1.

• A. 8.2 × 10^-3 Kg/m³
• B. 8.2 × 10³ Kg/m³
• C. 8.2 × 10² Kg/m³
• D. 4.1 × 10³ Kg/m³

Answer 1

The correct option is B

8.2 × 10³ Kg/m³

The excess pressure inside a soap bubble is
$\Delta P=4\frac{S}{R}=\frac{4\times 0.03N{m}^{-1}}{7.5\times {10}^{-3}m}=16N{m}^{-2}$
The pressure due to 0.02 cm of the liquid column is
$\Delta$ P=h$\rho$ g
=$(0.02\times {10}^{-2}m)\rho \left(9.8m{s}^{-2}\right)$
Thus,$16N{m}^{-2}=(0.02\times {10}^{-2}m)\rho \left(9.8m{s}^{-2}\right)$
or, $\rho =8.2\times {10}^{3}kg{m}^{-3}$