Question

When a capillary tube of diameter $0.8mm$ is dipped in a liquid having density $800kg{m}^{-3}$ then the height of liquid in the capillary tube rises to $4cm$. The surface tension of liquid is $(g=9.8m/s^2):$

• A. $4.3\times {10}^{-2}N{m}^{-1}$
• B. $5.6\times {10}^{-2}N{m}^{-1}$
• C. $6.3\times {10}^{-2}N{m}^{-1}$
• D. $7.3\times {10}^{-2}N{m}^{-1}$

Answer 1

Answer: (C)

Given that
Density of liquid $(D)=800kg{m}^{-3}$
Height of liquid $(h)=4cm=0.04m$
Acceleration due to gravity $(g)=9.8m/s^2$
Diameter of tube $(d)=0.8mm$
Radius of tube $(r)=0.4mm=4\times 10^{-4}m$
Surface tension $(T)=?$
By using
$T=\frac{rhDg}{2}$
$=\frac{\left(4\times 10^{-4}\right)\times (.04)\times 800\times 9.8}{2}$
$=4\times 10^{-4}\times .04\times 400\times 9.8$
$=4\times 4\times 4\times 98\times 10^{-5}$
Hence, $T=6.272\times 10^{-2}$
$=6.3\times 10^{-2}N{m}^{-1}$