A soap bubble, having radius of 1mm, is blown from a detergent solution having a surface tension of 2.5 xx 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

A soap bubble, having radius of 1mm, is blown from a detergent solutio

1.	A soap bubble, having radius of 1mm, is blown from a detergent solution having a surface tension of 2.5 xx 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
Answer» 0.5cm 100cm 10cm 1cm Solution :Here, R=mm `=1 xx 10^(-1) CM= 1 xx 10^(-3)m` Density of water `rho= 10^(3) kgm^(-3)` `h= Z_(0)` `T= 2.5 xx 10^(-2) N//m` `G= 10 ms^(-2)` Pressure inside the bubble, formed in air, `P_(i) = P_(0) + (4T)/(R )= P + (4T)/(R )` ...(1) (Where P= atmospheric pressure) If pressure at depth `Z_(0)` from the free SURFACE of water is P. then, `P.= P + rho gh= P + rho g Z_(0)` ...(2) Comparing equations (1) and (2), `rho g Z_(0) = (4T)/(R )` `:. Z_(0) = (4T)/(rho gR) = (4 xx 2.5 xx 10^(-2))/(10^(3) xx 10 xx 1 xx 10^(-3))` `:. Z_(0) = 10^(-2)m= 1cm`