devarshi-dt-logo

Question:

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 :

100cm

10cm

1cm

0.5cm

Solution:

Correct option is C. 1cm
Excess pressure = 4T/R,
Gauge pressure = ρgZ₀
Now, P₀ + 4T/R = P₀ + ρgZ₀
Z₀ = 4T/(Rρg)
Z₀ = 4 × 2.5 × 10⁻² / (10⁻³ × 10³ × 10)
Z₀ = 1cm