When one end of a tube of radius r is immersed vertically in a liquid of density `rho`, surface tension S, the rise of liquid in the tube is h and angle of contact is `theta` . If the tube is broken and its length is made `h' (lt h)`, then find the value of height of rise of liquid in the tube and angle of contact.

Explanation

When a capillary tube is broken at a height `h' ( lt h)`, the height of liquid column in the tube will be h' but the angle of contact `theta'` will change
As `h=(2S cos theta)/(r rho g)`
or ` (h)/(cos theta) = (2S)/(r rho g) `= a constant
`:. h/(cos theta)=(h')/(cos theta') or cos theta' = (h')/(h) cos theta`
or `theta' = cos ^(-1) ((h')/(h) cos theta)`.