A soap bubble, having radius of 1 mm, is blown from a detergent solution having a surface tension of 2.5 × 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 :

CONCEPT:

Surface tension: Surface tension is defined as the property of the liquid that are from the force of attraction on the surafce layer which minimize the surface area and its dimensions are force per unit area. 

As we known that the surface tension, the pressure which is outside the bubble is equal the the inside the bubble and it is wriiten as;

\({P_0} + \frac{{4T}}{R} = {P_0} + \rho g{Z_0}\)      -----(1)

CALCULATION:

Given: Tension, T = 2.5 × 10−2 N/m

g = 10 m/s²

Density of water, \(\rho\) = 103 kg/m3

radius, R = 1 mm

As we know that the pressure inside the surface is equal to below the free surface of water in a container therefore,the equation 1) becomes,

\( \frac{{4T}}{R} = \rho g{Z_0}\)

⇒ \( {Z_0}= \frac{{4T}}{R\rho g} \)

Now, on putting all the given values we have;

\({Z_0} = \frac{{4 \times 2.5 \times {{10}^{ - 2}}}}{{{{10}^{ - 3}} \times 1000 \times 10}}~~m\)

⇒ \({Z_0} = 10^{-2}\)  m

⇒ Z0 = 1 cm

Hence, option 3) is the correct answer.