Mechanical Properties of Fluids - Result Question 15

15. A soap bubble, having radius of $1 mm$, is blown from a detergent solution having a surface tension of $2.5 \quad 10-2 N / m$. The pressure inside the bubble equals at a point $Z_0$ below the free surface of water in a container. Taking $g=10 m / s^{2}$, density of water $=10_3 kg / m_3$, the value of $Z_0$ is :

[2019]

(a) $100 cm$

(b) $10 cm$

(c) $1 cm$

(d) $0.5 cm$

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Answer:

Correct Answer: 15. (c)

Solution:

  1. (c) Pressure inside the soap bubble

$=P_0+\frac{4 T}{R}$

And pressure at a point below the surface of water $=\rho g Z_0+P_0$

[where $P_0=$ atmospheric pressure]

By equating these pressure we get,

$P_0+\frac{4 T}{R}=P_0+\rho g Z_0$

$Z_0=\frac{4 T}{R \times \rho g}$

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

$Z_0=1 cm$