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 Z 0 below the free surface of water in a container. Taking g = 1 0 m / s 2, density of water = 1 0 3 kg / m 3, the value of Z 0 is:

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 Z 0 below the free surface of water in a container. Taking g = 1 0 m / s 2, density of water = 1 0 3 kg / m 3, the value of Z 0 is: (A) 1 cm (B) 0.5 cm (C) 100 cm (D) 10 cm

Tardigrade Admin · Accepted Answer

Excess pressure = (4T/R) , Gauge pressure = ρ g Z0 P0 + (4T/R) = P0 + ρ qZ0 Z0 = (4T/R ×ρ g) Z0 = (4×2.5 ×10-2/10-3 ×1000 ×10) m Z0 = 1 cm

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

1 cm

0.5 cm

100 cm

10 cm

Excess pressure = R4T​ , Gauge pressure =ρgZ0​ P0​+R4T​=P0​+ρqZ0​ Z0​=R×ρg4T​ Z0​=10−3×1000×104×2.5×10−2​m Z0​=1cm

Excess pressure = $\frac{4 T}{R}$ , Gauge pressure $= ρ g Z_{0}$
$P_{0} + \frac{4 T}{R} = P_{0} + ρq Z_{0}$
$Z_{0} = \frac{4 T}{R \times ρ g}$
$Z_{0} = \frac{4 \times 2.5 \times 1 0 ^{- 2}}{1 0 ^{- 3} \times 1000 \times 10} m$
$Z_{0} = 1 c m$