Question

A liquid column of height \(0.04 \, \text{cm}\) balances excess pressure of a soap bubble of certain radius. If density of liquid is \(8 \times 10^3 \, \text{kg m}^{-3}\) and surface tension of soap solution is \(0.28 \, \text{N m}^{-1}\), then diameter of the soap bubble is _________ \(\text{cm}\).
\((\text{if } g = 10 \, \text{m s}^{-2})\)

Answer 1

Correct Answer: 7

The excess pressure for a soap bubble is given by:
\[p = \frac{4S}{R}.\]
Using hydrostatic pressure:
\[p = \rho g h.\]
Equating the two:
\[\frac{4S}{R} = \rho g h \implies R = \frac{4S}{\rho g h}.\]
Substitute values:
\[R = \frac{4 \times 0.28}{8 \times 10^3 \times 10 \times 4 \times 10^{-4}}.\]
\[R = \frac{0.28}{8 \times 10^{-2}} = 3.5 \, \text{cm}.\]
The diameter is:
\[\text{Diameter} = 2R = 7 \, \text{cm}.\]
Final Answer: $7 \, \text{cm}$.