A vertical capillary tube is filled with wate | vedclass

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(D) When the finger is removed,the water column is supported by the surface tension forces at both the upper and lower menisci.The total upward force

Vedclass · Accepted Answer

Only $2.86 \,\, cm$ of water will stay in the capillary and the rest will fall down.

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(D) When the finger is removed,the water column is supported by the surface tension forces at both the upper and lower menisci.The total upward force due to surface tension is $F_{up} = 2 \pi r T + 2 \pi r T = 4 \pi r T$.The downward force due to the weight of the water column is $F_{down} = Mg = V ho g = \pi r^2 h ho g$.For equilibrium,$F_{up} = F_{down}$,so $4 \pi r T = \pi r^2 h ho g$.Solving for height $h$,we get $h = \frac{4 T}{r ho g}$.Given $T = 70 \,\, dyne/cm$,$r = 1 \,\, mm = 0.1 \,\, cm$,$ho = 1 \,\, g/cm^3$,and $g = 980 \,\, cm/sec^2$:$h = \frac{4 	imes 70}{0.1 	imes 1 	imes 980} = \frac{280}{98} = 2.857 \approx 2.86 \,\, cm$.Thus,only $2.86 \,\, cm$ of water will stay in the capillary and the rest will fall down.

$A$ vertical capillary tube is filled with water up to the top after closing its lower end with a finger. If the finger is removed,we shall observe that: ($T = 70 \,\, dyne/cm$,radius of capillary $r = 1 \,\, mm$ and $g = 980 \,\, cm/sec^2$)

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