A capillary tube of radius' $r$' 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):

$h=\frac{2\alpha }{dgr}$

hence work done by force of surface tension is

$W_s=\alpha \times 2\pi r\times h=\frac{4\pi {\alpha }^2}{dg}$

But centre of mass of liquid in the capillary tube is at a height $h / 2$. Hence potencial energy gained

$=\frac{Mgh}{2}=\pi r^2\times h\times d\times g\times \frac{h}{2} =\frac{2\pi {\alpha }^2}{dg}$

Hence work done by gravity $=-\frac{2\pi {\alpha }^2}{dg}=$ Amount of heat developed $=\frac{2\pi {\alpha }^2}{dg}$