A glass rod of diameter $d = 2 m m$ is inserted symmetrically into a glass capillary tube of radius $r = 2 m m$ . Then the whole arrangement is vertically dipped into liquid having surface tension $0.072 N / m$ . The height to which liquid will rise on capillary is (Take $g = 10 m s /^{2}, p_{l i q} = 1000 k g /^{3}$ . Assume contact angle to be zero of capillary tube to be long enough).

1.44 c m

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6 c m

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4.86 c m

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None of these

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Solution

The correct option is A $1.44 c m$
Upward force due to surface tension supports the weight of liquid column of height $h$ .
Surface tension force $= T (2 π r_{1} + 2 π r_{2})$
Weight of liquid column $= h (π {r_{2}}^{2} - π {r_{1}}^{2}) ρ g$
$\Rightarrow T (2 π r_{1} + 2 π r_{2}) = h (π {r_{2}}^{2} - π {r_{1}}^{2}) ρ g \Rightarrow 2 T π (r_{1} + r_{2}) = h π (r_{2} + r_{1}) (r_{2} - r_{1}) ρ g \Rightarrow h = \frac{2 T}{(r_{2} - r_{1}) ρ g} \Rightarrow h = \frac{2 \times 0.072}{(2 - 1) \times 10^{- 3} \times 1000 \times 10} \Rightarrow h = 0.0144 m = 1.44 c m$

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Q. A glass rod of radius

1 m m

is inserted symmetrically into a glass capillary tube with inside radius

2 m m

. Then the whole arrangement is brought in contact of the surface of water. Surface tension of water is

7 \times 10^{- 2} N / m

. To what height will the water rise in the capillary?

(θ = 0^{\circ})

A glass rod of radius 1mm is inserted symmetrically into a glass capillary tube with inside radius 2mm Then the whole arrangement is brought in contact with the surface of water.Surface tension of water is $7 \times 10^{- 2} N / m$ .To what height will water rise in the capillary $(θ = 0^{o})$