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Question: Mercury has an angle of contact equal to \(140^{o}\)with soda lime glass. A narrow tube of radius l ...

Mercury has an angle of contact equal to 140o140^{o}with soda lime glass. A narrow tube of radius l mm made of this glass is dipped in a trough containing mercury. The surface tension of mercury at the temperature of the experiment is 0.465Nm−10.465Nm^{- 1} The distance by which the mercury dip down in the tube relative to the mercury surface outside is

(Density of mercury =13.6×103kgm−3= 13.6 \times 10^{3}kgm^{- 3})

A

5.345.34 mm

B

2.352.35 mm

C

6.256.25 mm

D

1.441.44 mm

Answer

5.345.34 mm

Explanation

Solution

Here, θ=140º,r=1×10−3m\theta = 140º,r = 1 \times 10^{- 3}m

S=0.465Nm−1,ρ=13.6×103kgm−3S = 0.465Nm^{- 1},\rho = 13.6 \times 10^{3}kgm^{- 3}

Ash=2Scos⁡θrρg=2×0.465×(−cos⁡40º)10−3×13.6×103×9.8h = \frac{2S\cos\theta}{r\rho g} = \frac{2 \times 0.465 \times ( - \cos 40º)}{10^{- 3} \times 13.6 \times 10^{3} \times 9.8}

(∵cos⁡140º=−cos⁡40º)(\because\cos 140º = - \cos 40º)

=−5.34×10−3m=−5.34mm= - 5.34 \times 10^{- 3}m = - 5.34mm

Note negative value of h shows that the mercury level is depressed in the tube.