When water is filled caerfully in a glass . One can fill it to a height h above the rim of glass due to the surface tension of water . To calculate h just before water starts flowing model the shape of the water above the rim as a disc of thickness h having semicircular edges as shown achematically in the figure When the pressure of water at the bottom of this disc exceeds what can be withstood due to the surface lension , the water surface breaks near the rim and water starts flowing form there if the density of water, its surface tension and the acceleration due to gravity are `10^(3)kgm^(-3),0.07Nm^(-1)and10ms^(-2)` , respectively, the value of h (in mm) is _________

Answer

5.29

Explanation

`P_(0)rhogh(2T)/(r )=P_(0)`
`rhoph=(T)/(R )`
`rhogh=(T)/(h)xx2`
`h^(2)=(4T)/(rhog)=(2xx0.07)/(10^(3)xx10)`
`h=sqrt(14)=3.74xx10^(-3)`
alternative
`T(2r)=(rhogh)/(2)(2r)h`