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Question
A capillary of diameter d mm is dipped in water such that the water rises to a height of 30 mm. If the radius of the capillary is made `(2/3)` of its previous value, then compute the height up to which water will rise in the new capillary?
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Solution
Let diameter of capillary tube = d mm
Let the radius of capillary tube r1 = r mm
Capillary rise h1 = 30 mm
Let the radius of another capillary tube r2 = `2/3` r
Let the capillary rise of another capillary tube be h2
We know that
T = `("hr"ρ"g")/2`
∴ `"h" ∝ 1/"r"`
`"h"_1/"h"_2 = "r"_2/"r"_1`
`30/"h"_2 = (2/3 "r")/"r"`
`30/"h"_2 = 2/3`
∴ h2 = `(3 xx 30)/2` = 45 mm
Capillary rise in the new capillary tube = 45 mm
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