JEE Main 2016 · Physics · Fluid Mechanics, Elasticity and Surface Tension · easy

A capillary tube of inner radius 0.5 mm (zero angle of contact) is dipped in water of surface tension 0.07 N m^-1 and density 1000 kg m^-3, and is…

Single correct option

A capillary tube of inner radius

0.5\ \mathrm{mm}

(zero angle of contact) is dipped in water of surface tension

0.07\ \mathrm{N\,m^{-1}}

and density

1000\ \mathrm{kg\,m^{-3}}

, and is then inclined at

60^\circ

to the vertical. Taking

g=10\ \mathrm{m\,s^{-2}}

, the length of the water column inside the tilted tube, measured along the tube from the free water surface outside, is

Show answer and solution

Answer: (C) $5.6\ \mathrm{cm}$

The vertical height of rise does not depend on the inclination of the tube:

h=\dfrac{2S\cos\theta}{r\rho g}=\dfrac{2\times0.07}{0.5\times10^{-3}\times1000\times10}=0.028\ \mathrm{m}=2.8\ \mathrm{cm}

. When the tube makes an angle

\alpha=60^\circ

with the vertical, the meniscus must still be at the same vertical height

h

, so the length of liquid along the tube is

l=\dfrac{h}{\cos\alpha}=\dfrac{2.8}{0.5}=5.6\ \mathrm{cm}

. Quoting

2.8\ \mathrm{cm}

forgets that the column is slanted, while

h\cos60^\circ=1.4\ \mathrm{cm}

multiplies by the wrong factor.

Original question written in the JEE Main 2016 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake