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Water rises up in a glass capillary upto...

Water rises up in a glass capillary upto a heigh 10 cm, while mercury falls down by 3.5 cm in the same capillary. If the angles of contact for water-glass and mercury-glass are taken as `0^(@)` and `135^(@)` respectively, compare the surface tensions of water and mercury. [Given density of water = `10^(3)` kg `m^(-3)`, density of mercury = 13.6 `xx 10^(3)` kg `m^(-3)`]

Text Solution

Verified by Experts

For water, `h_(1) `= 10 cm
0.1 m
Density `rho_(1), = 10^(3) kg m^(-3)`
Let the radius of the capillary be = r
Applying the formula h,p,g =`(2S_(1)costheta_(1))/r`
`S_(1) = (h_(1) rho_(1) gr)/(2cos0^(@))`
`S_(1) = 100 (gr)/2`
For mercury,`h_(2) = -3.5cm`
= -0.035m
Density `rho_(2) = (13.6xx10^(3) gr)/(2cos(135))`
0.67` (gr)/2 ` 10^(3)
`S_(2) = 670 (gr)/2`
Comparing equations (i) and (ii), we get `S_(1)/S_(2) = 100/670 = 1/6.7 `
This is the required ratio.
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