Question

A long capillary tube of radius 1 mm open at both ends are filled with water and placed vertically. What will be the height of column of water left in capillary ? The thickness of wall of capillary is negligible. (surface tension of water $= 73.5 \times 10^{-3} N/m$ density of water $= 10^3 \,kg/m)$

• A. 3 cm
• B. 1.5 cm
• C. 4.5 cm
• D. 6 cm

Answer 1

Answer: (A)

The liquid rises to such a height, that external pressure balances internal pressure. The column of liquid remaining in the tube will be held by two meniscus an upper and lower one. Therefore height of column of water left in the tube will be
$ \frac{2 T}{r}+\frac{2 T}{r}=h \rho g $
$\Rightarrow \frac{4 T}{r}=h \rho g $
$ \Rightarrow h=\frac{4 T}{r \rho g} $
Given, $ T=73.5 \times 10^{-3} N / m , $
$ r=1\, mm =1 \times 10^{-3} m , $
$ \rho=10^{3} kg / m , $
$ g=9.8 \,m / s ^{2} $
$ \therefore h=\frac{4 \times 73.5 \times 10^{-3}}{1 \times 10^{-3} \times 9.8 \times 10} $
$ \Rightarrow h=3 \times 10^{-2} m =3 \,cm$