If the excess pressure inside a soap bubble of radius 3 ~mm is equal to the pressure of a water column of height 0.8 ~cm , then the surface tension of the soap solution is ( _ water =1000 ~kg / m ^3, g=9.8 ~m / s ^2 )

Step-by-step solution

The excess pressure inside the bubble is given as, P= 4 T r as the soap bubble has two liquid-gas interfaces. The pressure to height column of water is given as, P= h g Since the excess pressure inside the bubble is balanced by the height of the column and it can be written as, 4 T r = h g T= r h g 4 On plugging the given values: T= 1 4 (3 10⁻³ ~m 10^3 ~kg ~m ^3 8 10⁻³ ~m 9.8 m s ^2 )=58.8 10⁻³ ~N / m