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(D) The condition for water not to leak through the holes is that the pressure exerted by the water column must be balanced by the capillary pressure

Vedclass · Accepted Answer

$30$

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(D) The condition for water not to leak through the holes is that the pressure exerted by the water column must be balanced by the capillary pressure (excess pressure) at the hole.Excess pressure $P = \frac{2T}{r}$,where $T$ is the surface tension and $r$ is the radius of the hole.The pressure due to the water column is $P = h ho g$.Equating the two,we get $h ho g = \frac{2T}{r}$.Given: Diameter $d = 0.1 \, mm = 0.01 \, cm$,so radius $r = 0.005 \, cm$.Surface tension $T = 75 \, dyne/cm$.Density of water $ho = 1 \, g/cm^3$.Acceleration due to gravity $g = 1000 \, cm/s^2$.Substituting the values: $h = \frac{2T}{r ho g} = \frac{2 	imes 75}{0.005 	imes 1 	imes 1000} = \frac{150}{5} = 30 \, cm$.

$A$ vessel,whose bottom has round holes with a diameter of $0.1 \, mm$,is filled with water. The maximum height to which the water can be filled without leakage is ....... $cm$ (Surface Tension of water = $75 \, dyne/cm$,$g = 1000 \, cm/s^2$).

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