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:
- (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,
$P_0+\frac{4 T}{R}=P_0+\rho g Z_0$
$Z_0=\frac{4 T}{R \times \rho g}$
$Z_0=\frac{4 \times 2.5 \times 10^{-2}}{10^{-3} \times 1000 \times 10} m$
$Z_0=1 cm$
