Question

Water rises to a height of 6.6 cm in a capillary tube of radius 0.2mm the surface tension of water is

Answer 1

Explanation:

rho = density of water

r = radius of capillary tube

h= height of water

g=acceleration due to gravity (10 m/s^2)

x = angle of contact =0 for water-glass

surface tension = h*r*rho*g/(2*cos x)

= 0.066*0.0002*1000*10/(2*1)

= 0.066 N/m

Answer 2

Note: The correct question must be provided with following options-

Water rises to a height of $6.6 cm$ in a capillary tube of radius $0.2mm$ the surface tension of water is-

a) $6.5\times 10^{-3}N/m$

b) $6.5\times 10^{-2}N/m$

c) $6.5\times 10^{-4}N/m$

d) $6.5\times 10^{-1}N/m$

Explanation for correct option

b:

Step 1: Given data

radius, $r=0.2mm=2\times 10^{-4} m$

height, $h=6.6cm=0.066m$

surface tension, $\gamma=?$

Step 2: Calculating the surface tension

We know that,

$\gamma=\frac{rh\rho g}{2}$

$\rho=1008kg/m^{3}$

$g=10m/s^{2}$

$\gamma=\frac{2\times 10^{-4}\times 0.066\times 1008\times 10 }{2}=66.5\times 10^{-3}$

$\gamma=6.65\times 10^{-2}\approx 6.5\times 10^{-2}N/m$

Thus, surface tension of water is $6.5 \times 10^{-2}N/m$.

Explanation for incorrect options

a,c,d:

The surface tension of water is not equal to $6.5\times 10^{-3}N/m$ , $6.5\times 10^{-4}N/m$ or $6.5\times 10^{-1}N/m$.

Thus, options a,c and d are incorrect.

Hence, option b) is correct.

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