A vessel whose bottom has round holes with diameter of $1 m m$ is filled with water. Assuming that surface tension acts only at holes, then the maximum height to which the water can be filled in vessel without leakage is
(Given surface tension of water is $75 \times 10^{- 3} N / m$ and $g = 10 m / s^{2}$ )

3 c m

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0.3 c m

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3 m m

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3 m

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Solution

The correct option is A $3 c m$
Using formula
$h = \frac{2 T cos θ}{ρ r g}$
= $\frac{2 \times 75 \times 10^{- 3} \times 1}{1000 \times \frac{1}{2} \times 10^{- 3} \times 10} (cos 0^{o} = 1)$
$= 0.03 m = 3 c m$

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Q. A vessel whose bottom has round hole with diameter of

1 m m

is filled with water. Only surface tension acts at hole. (Surface tension of water is

75 \times 10^{- 3}

N/m and

g = 10 m / s^{2}

). The maximum height (in

c m

) to which water can be filled in the vessel without leakage is:

A bowl whose bottom has a round hole of diameter $1 mm$ is filled with water. Assuming that surface tension acts only at hole, find the maximum height (in $cm$ ) up to which water can be filled in the vessel without leakage. (Given, surface tension of water $= 75 \times 10^{- 3} {Nm}^{- 1}, g = 10 {ms}^{- 2}$ and density of water $1000 {kg/m}^{3}$ ).
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