The rise of a liquid in a capillary tube depends on

Explanation

Let, the liquied meniscus in the tube is along the circle of circumference `(2 pi r)`. Due to surface tentio of water a force equal to t acts on unit length acts tangentially to the liquid surface, at n angle `theta` with wall of capillary tube directed inwards.
According to Newton's third of motion tube exert an equal and opposite reaction R.
(i) Vetical component : `T cos theta`, which is in vertically upward direction.
(ii) Horizontal component : ` T sin theta`, which is acting radially outward along horizontal direction.
Total vartical upward force acting on the liquid column inside the capillary.
`=T cos theta xx2pir`.
where `,2 pi r` is the circumference of mensicus.
Let, v be the volume of the liquid rise in the tube upto 'h' then,
`V=pir^(2)h`
`:.` Weight of liquid column in capillary tube =maxx `xx` accleleration due to gravity
`W=mg`
`rho=Vg`
`=rho pi r^(2)hg`
where, `rho`= density of liquid m= mass of liquid.
Total upward force = Total downward force
`2pi r T cos theta = rho pi r^(2) hg`
`T=(rhg rho)/(2 cos theta)`
`h=(2T cos theta)/(r rho g)`