Question

Water rises in a capillarity tube to a height 2.0 cm. if the tube is inclined at an angle of 60° with the vertical, what will be the length of the water column within the tube?

• A. 4 cms
• B. cms
• C. 1 cm
• D. None of these

Answer 1

The correct option is A

4 cms

When the tube is vertical, the column of liquid in the tube is kept up only by the force of adhesion between the tube and the water.

where $F_A$ is the adhesive force
$F_A=2\pi rScos\theta$
For equilibrium
$Mg=2\pi rScos\theta$
$\Rightarrow \pi r^2{h}_1\rho g=2\pi rScos\theta$
$\Rightarrow h_1=\frac{2\pi rScos\theta }{\pi r^2\rho g}=\frac{2Scos\theta }{r\rho g}$
When it is inclined


Due to equilibrium
$N=Mgsin{60}^{\circ }$
$\Rightarrow N=\pi r^2{h}_2\rho gsin{60}^{\circ }=\pi r^2{h}_2\rho g\frac{\sqrt{3}}{2}.......\left(1\right)$
$F_A=Mgcos{60}^{\circ }$
$F_A=\pi r^2{h}_2\rho g\frac{1}{2}$
$\Rightarrow h_2=\frac{2\pi rScos\theta }{\pi r^2\rho g}\times 2$
$=\left[\frac{2s\cos \theta }{r\rho g}\right]\times 2$
$=4cm$