A glass rod of radius ' r ' ' is inserted symmetrically into a vertical capillary tube of radius ' r ₂ ' ( r ₁ < r ₂ ) such that their lower ends are at same level. The arrangement is dipped in water. The height to which water will rise into the tube will be ( = density of water, T = surface tension in water, g = acceleration due to gravity)

Step-by-step solution

Vertical component of total force of surface tension F = ( r ₂+ r ₁ ) 2 T Weight of the liquid in the capillary W = ( r ₂^2- r ₁^2 ) h g This is balanced by the vertical component of the face due to the surface tension ( r ₂^2- r ₁^2 ) h g = ( r ₂+ r ₁ ) 2 T Simplifying and solving for h we get, h = 2 ~T ( r ₂- r ₁ ) g = 2 ~T ( r ₂- r ₁ ) g (For pure water, =0^ , =1 )