Question

A capillary tube of length $l=50cm$ and radius $r=\frac{1}{4}mm$ is immersed vertically into water. Find the capillary rise if angle of contact $=0^{\circ }$ and coefficient of surface tension $=72dyne/cm.$ (Take $g=1000cm/s^2$).

• A. $45.8cm$
• B. $35.4cm$
• C. $50cm$
• D. $30.6cm$

Answer 1

The correct option is C $50cm$

In a capillary tube of radius $r$ the rise or fall of the level is given by
$h=h_0=\frac{2T\cos \theta }{\rho gr}\dots \left(i\right)$
Where, $T=$ Surface tension,
$\theta =$ angle of contact,
$\rho =$ density of liquid,
$g=$ Acceleration due to gravity Substituting the values in equation $\left(i\right)$, we get
$h_0=\frac{2\left(72\right)\cos 0^{\circ }}{\left(1\right)\left(1000\right)\left(\frac{1}{40}\right)}=57.6cm$
Since, $l(=50cm)<h_0$
$h=50cm$
Final answer: $\left(d\right)$