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Question

Two capillary tubes are dipped in the liquid of densities in the ratio 5:2 and the heights of liquids in the two tubes are 2cm and 3cm respectively. If surface tensions of liquids are 75 and 70 dyne/cm respectively. Assume the angles of contacts are same then ratio of the radii is

A
7:5
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B
5:7
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C
14:15
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D
9:14
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Solution

The correct option is C 9:14
By using rise in capillary tube formula, h=2Tcosθρgr
where, h is rise of water in capillary
T is surface tension of water
ρ is density of water
g is acceleration due to gravity
r is radius of capillary
So, hA=2TAcosθρArAg=2 ................(1)

hA=2TBcosθρBrBg=2 ................(2)
Dividing (1) and (2) we get:
23=TAρBrBρArATB
rArB=75×3×270×2×5=914

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