Question

A soap bubble, having radius of 1 mm, is blown from a detergent solution having a surface tension of 2.5 x 10⁻² N/m. The pressure inside the bubble equals at a point Z₀ below the free surface of water in a container. Taking g = 10 m/s² density of water = 10³ kg/m³, the value of Z₀ is :
(1) 100 cm
(2) 10 cm
(3) 1 cm
(4) 0.5 cm

Answer 1

Excess pressure = 4T/R

Gauge pressure = ρρgZ

Now,

Po + 4T/R = Po + pgZo

Zo = 4T/R×ρg

Zo = {4×2.5×10^(-2)}/[10^(-3)×1000×10]

Zo = 1cm

Answer 2

The value of $\bold{Z_{o}}$ value is 1 cm.

Step by step explanation:

Gauge pressure:

The excess pressure above the atmospheric pressure is called gauge pressure.

From the  given,

Radius of soap bubble = 1mm

Surface tension of solution = $2.5\times 10^{-2}N/m$

The given condition-

The pressure inside the bubble equals at a point Z₀

Excess pressure can be calculated by the following formula.

$\bold{Excess\,presure=\frac{4T}{R}}$....................(1)

Gauge pressure can be calculated by the following formula.

$\bold{Gauge\,presure=\rho g Z_{o}}$................(2)

Now equating (1) and (2)

$\bold{P_{o}+\frac{4T}{R}=P_{o}+\rho g Z_{o}}$

$Z_{o}=\frac{4T}{R\times \rho g}$

$= \frac{4\times 2.5 \times 10^{-2}}{10^{-3}\times 1000 \times 10}=1cm$

Therefore, The value of $\bold{Z_{o}}$ value is 1 cm.