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In a capillary tube of radius 'R' a stra...

In a capillary tube of radius 'R' a straight thin metal wire of radius 'r' (`Rgtr)` is inserted symmetrically and one of the combination is dipped vertically in water such that the lower end of the combination Is at same level . The rise of water in the capillary tube is [T=surface tensiono of water `rho` =density of water ,g =gravitational acceleration ]

A

`(T)/((R+r)rho g)`

B

`(R rho g)/(2T)`

C

`(2T)/((R-r)rho g)`

D

`((R-r )rho g)/(T)`

Text Solution

Verified by Experts

The correct Answer is:
C
According to question, rise of water in the capillary tube is given by
`h = (2T cos theta)/(rho g(R-r))`
[Symbols have their usual meanings]
In the given case,
`cos theta = 1` as `theta = 0^(@)`
So, `h = (2T)/(rho g(R-r))`
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Knowledge Check

  • In a capillary tube of radius 'R' a straight thin metal wire of radius ' r ' (R gt r) is inserted symmetrically and one end of the combination is at the same level . The rise of water in the capillary tube is

    A
    `T/((R+r)rhog)`
    B
    `(Rrhog)/(2T)`
    C
    `(2T)/((R-r)rhog)`
    D
    `((R-r)rhog)/T`

  • A glass rod of radius r_(1) is inserted symmetrically into a vertical capillary tube of radius r_(2) such that their lower ends are at the same level. The arrangement is now dipped in water. The height to which water will rise into the tube will be ( sigma = surface tension of water, rho = density of water)

    A
    `(2sigma)/((r_(2)-r_(1))rhog)`
    B
    `sigma/((r_(2)-r_(1))rhog)`
    C
    `(2sigma)/((r_(2)+r_(1))rhog)`
    D
    `(2sigma)/((r_(2)^(2)+r_(1)^(2))rhog)`

  • When one end of a capillary tube is dipped vertically in water, the pressure below the meniscus of water is

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    more than upper side pressure
    B
    lesser than upper side pressure
    C
    equal to atmospheric
    D
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