Question

The lower end of a glass capillary tube is dipped in water. Water rises to a height of $8 cm .$ The tube is then broken at a height of $4 cm .$ The height of water column and angle of contact will be.

• A. $2 cm , 60^{\circ}$
• B. $4 cm , 120^{\circ}$
• C. $4 cm , 60^{\circ}$
• D. $2 cm , 30^{\circ}$

Answer 1

Answer: (C)

Water rises in capillary tube due to force of adhesion between solid and liquid molecules. Tube is broken at height of $4 cm$, so force of adhesion is present till $4 cm$.
So height of water column is $4 cm$.
$\therefore \frac{ h }{\cos \theta}=\frac{ h _{1}}{\cos \theta'}\left(\frac{ h }{\cos \theta}=\frac{2 S }{\rho rg }\right)$
$\therefore \frac{8}{\cos 0^{0}}=\frac{4}{\cos \theta}$
$\Rightarrow \cos \theta=\frac{1}{2}$
$ \Rightarrow \theta=60^{\circ}$