A cappillary tube of radiue `r` is lowered into water whose surface tension is `alpha` and density `d`. The liquid rises to a height. Assume that the contact angle is zero. Choose the correct statement (s):

Options

A. Magnitude of work done by force of surface tension is `(4pialpha^(2))/(dg)`
B. Magnitude of work done by force of surface tension is `(2pialpha^(2))/(dg)`
C. Potential energy acquired by the water is `(2pialpha^(2))/(dg)`
D. The amount of heat developed is `(2pialpha^(2))/(dg)`

Answer

A, C, D

Explanation

`h=(2alpha)/(dgr)`
hence work done by force of surrface tension is
`W_(S)=alphaxx2pirxxh=(4pialpha^(2))/(dg)`
But centre of mass of liquid in the capillary tube is at a hight `(h)/(2)`. Hence potential energy gained
`=(Mgh)/(2)=pir^(2)xxhxxdxxgxx(h)/(2)=(2pialpha^(2))/(gd)`
Hence work done by gravity `=(-(2pialpha^(2))/(dg))`
Amount of heat developed `=(2pialpha^(2))/(dg)`