A soap bubble, having radius of 1 mm, is blown from a detergent solution having radius of 1 mm is blown from a detergent solution having a surface tension of `2.5xx10^(-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 :

Options

A. 0.5cm
B. 100cm
C. 10cm
D. 1cm

Answer

D

Explanation

The pressure at a point `Z_(0)` below the surface of water, `P_(Z_(0)) = P_(0) + rho g Z_(0)`
Alsi, pressure inside a soap bubble, `P= P_(0) + (4T)/(R )`
As per question, `P_(Z_(0)) = P`
`:. P_(0) + (4T)/(R ) = P_(0) + rho gZ_(0)`
`Z_(0) = (4T)/(R rho g) = (4 xx 2.5 xx 10^(-2))/(1 xx 10^(-3) xx 10^(3) xx 10) = 1 xx 10^(-2) m=1cm`