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

100 cm

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75 cm

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50 cm

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30 cm

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Solution

The correct option is D
30 cm

Let 'N' number of holes are there on the bottom of the vessel Force due to water column = Force exerted due to the surface tension i.e., (Pressure)(Area)=(Surface tension)(Total circumference of holes)

$(h ρ g) N π r^{2}$ = $T (2 π r) N$

hρgr = 2T

h= $\frac{2 T}{ρ g r}$

= $\frac{2 \times 75}{1 \times 10^{3} \times 0.05 \times 10^{- 1}}$

=30 cm

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A vessel, whose bottom has round holes with diameter of 0.1mm, is filled with water. The maximum height to which the water can be filled without leakage is(S.T. of water =75 dyne/cm, g =1000 cm/s2)

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