Question

A capillary tube is vertically partly dipped in water shows capillary rise. If the mass of water in capillary rise is $22mg$. What is the diameter of tube ( $T=70dynes/cm$)

• A. $0.5mm$
• B. $1mm$
• C. $1.5mm$
• D. $2mm$

Answer 1

The correct option is B $1mm$

we know $\frac{m}{v}=\rho$

so, v = $\frac{m}{\rho }=\frac{22mg}{1000kg/m^3}=2.2\times {10}^{-8}{m}^3$

Now v of water in tube is $\pi r^{2}h$

where h = $\frac{2T}{\rho rg}$ (By capillary rise formula)

$\therefore v=\pi r^{2}h=\pi r^2\left(\frac{2T}{\rho rg}\right)$

$2.2\times 10-5=\pi r\frac{2T}{\rho g}$

$r=\frac{2.2\times {10}^{-8}\times 1000\times 10\times {10}^{-2}}{\frac{22}{7}\times 2\times 70\times {10}^{-5}}$ (taking $\pi =\frac{22}{7}$)

$=\frac{1}{2}\times {10}^{-3}m$

$=0.5mm$

So, diameter $=2r=1mm$