__Question 10.29__:
Mercury
has an angle of contact equal to 140° with soda lime glass. A
narrow tube of radius 1.00 mm made of this glass is dipped in a
trough containing mercury. By what amount does the mercury dip down
in the tube relative to the liquid surface outside? Surface tension
of mercury at the temperature of the experiment is 0.465 N m

^{–1}. Density of mercury = 13.6 × 10^{3}kg m^{–3}.

__Solution__:*θ*= 140°

Radius of the narrow tube,

*r*= 1 mm = 1 × 10

^{–3}m

Surface tension of mercury at the given temperature,

*s*= 0.465 N m

^{–1 }

Density of mercury,

*ρ*=13.6 × 10

^{3}kg/m

^{3}

Dip in the height of mercury =

*h*

Acceleration due to gravity, g = 9.8 m/s

^{2}

Surface tension is related with the angle of contact and the dip in the height as:

s = hρgr / 2 Cosθ

∴ h = 2s Cosθ / ρgr

= 2 X 0.465 X Cos140

^{0}/ (1 X 10

^{-3}X 13.6 X 10

^{3}X 9.8)

= -0.00534 m

= -5.34 m

Here, the negative sign shows the decreasing level of mercury. Hence, the mercury level dips by 5.34 mm.

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