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A long capillary tube of radius r = 1 mm...

A long capillary tube of radius `r = 1 mm` open at both ends is filled with water and placed vertically. What will be the height (in `cm`) of the column of water left in the capillary walls is negligible. (surface tension of water is `72 "dyne"//"cm"` and `g = 1000 "cm"//"sec"^(2)`)

Text Solution

Verified by Experts

The correct Answer is:
`2.8cm`
Weight of liquid `=` surface tension force
`pir^(2)hdg = alpha2pir`
`h = (2alpha)/(dgr)`
work done by surface tension force `= (alpha. 2pir)h = (4pialpha^(2))/(dg)`
potential energy liquid `= mg h//2 = pir^(2)h dg '(alpha)/(dgr) = (2pialpha^(2))/(dg)`
rest part of work done
i.e. `[(4pialpha^(2))/(dg)-(2pialpha^(2))/(dg)=(2pialpha^(2))/(dg)]` is lost the form of heat.
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Knowledge Check

  • What will be the difference of pressure inside and outside a drop of water of radius 1.0 mm ? (The surface tension of water is 73 dyne/cm-)

    A
    `146N//m^(2)`
    B
    `73N//m^(2)`
    C
    `7.3N//m^(2)`
    D
    `200N//m^(2)`

  • A glass capillary tube of internal radius r = 0.25 mm is immersed in water. The top end of the tube projected by 2 cm above the surface of the water. At what angle does the liquid meet the tube? Surface tension of water = 0.7 N/m.

    A
    `theta=90^(@)`
    B
    `theta =70^(@)`
    C
    `theta =45^(@)`
    D
    `theta =35^(@)`

  • The lower end of a capillary tube of radius r cm is placed vertically in water. What is the heat evolved if water rise upto a height h in the capillary tube ?

    A
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    B
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    C
    `-(pi^(2)r^(2)h^(2)g)/(2J)`
    D
    `(pir^(2)h^(2)g)/(2J)`

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