Water rises up to a height h in a capillary tube immersed vertically in water. When this whole arrangement is taken to a depth d in a mine, the water level rises up to a height h ′ . If R is the radiu

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Water rises up to a height h in a capillary tube immersed vertically in water. When this whole arrangement is taken to a depth d in a mine, the water level rises up to a height h ′ . If R is the radius of the earth, then the ratio h ′ h ​ is

TestHub · Accepted Answer

On the surface of the earth T = 2 r h ρ g ​ for water ∴ h = r ρ g 2 T ​ At a depth d , the value of acceleration due to gravity changes to g ′ = g ( 1 − R d ​ ) , therefore g ′ = g ( 1 − R d ​ ) , therefore ​ h ′ = r ρ g ′ d 2 T ​ = r ρ g ( 1 − R d ​ ) 2 T ​ ∴ h ′ h ​ = r ρ g 2 T ​ × 2 T r ρ g ( 1 − R d ​ ) ​ = 1 − R d ​ ​

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