A vessel whose bottom has round holes with diameter 0.1 mm is filled with water. The maximum height upto which water can be filled without leakage is ................. cm.
(Given: Surface Tension $=$ 7.5 x 10 $^{- 3}$ Nm $^{- 1}$ and g $=$ 10ms $^{- 2}$ )

100

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75

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50

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30

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Solution

The correct option is C $30$ cm
From the hole water bulges out in the shape of a hemisphere. The force of surface tension acts upwards along the surface of the hemisphere. For no leakage the pressure force of column should be equal to the surface tension force. Radius of the hole is $\frac{0.1}{2} m m$
Using the force balance at the interface we get
$2 π r σ = (h ρ g) (π r^{2})$
or
$h = \frac{2 σ}{r ρ g}$
or
$h = \frac{2 \times 7.5 \times 10^{- 3} \times 2}{0.1 \times 10^{- 3} \times 1000 \times 10} = 0.3 m = 30 c m$

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A vessel whose bottom has round holes with diameter 0.1 mm is filled with water. The maximum height upto which water can be filled without leakage is ................. cm.(Given: Surface Tension = 7.5 x 10−3 Nm−1 and g = 10ms−2)

A vessel whose bottom has round holes with diameter 0.1 mm is filled with water. The maximum height upto which water can be filled without leakage is ................. cm.
(Given: Surface Tension $=$ 7.5 x 10 $^{- 3}$ Nm $^{- 1}$ and g $=$ 10ms $^{- 2}$ )