Expression for the height of capillary rise between two parallel plates dipping liquid of density `sigma` separated by a distance d. The surface tension of the liquid is T. [Take angle of contact to be zero]

Options

A. `h=(2T)/(sigmadg)`
B. `h=(2d)/(sigmaT)`
C. `h=(sigmaT)/(d)`
D. `h=(2T^(2))/(sigmad)`

Answer

A

Explanation

The meniscus between two plates in cylindrical is shape. Pressure at A (the lowestpoint of the meniscus)
`p_(A)=p_(0)-(T)/(r)`
Pressure at `B=` pressure at `C=p_(0)=` pressure at `A+sigmagh`
`becauseP_(B)=p_(0)=p_(0)-(T)/(r)+sigmagh,h=(T)/(sigmagr)=(2T)/(sigmagd)`
Alternative method:
Force upward `=2lTcostheta=2lT(becausetheta=0^(@))`
Gravitational pull `=("Volume"xx"density")g=lhdsigmag`
`because2lT=lhdrhogimpliesh=(2T)/(dsigmag)`