A vessel whose bottom has a round hole with diameter 0.1 mm is filled with water. The maximum height up to which water can be filled without leakage is ............. cm (given surface tension $= 7.5 \times 10^{- 2} N m^{- 1}$ and $g = 10 m s^{- 2}$

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

Self-weight of water column is to be balanced with force due to the surface tension.

$T (2 π r) = m g T (2 π r) = ρ v g T (2 π r) = ρ A h g h = \frac{T (2 π r)}{ρ A g}$ ; $h = \frac{2 T}{ρ r g}$

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A vessel whose bottom has a round hole with diameter 0.1 mm is filled with water. The maximum height up to which water can be filled without leakage is ............. cm (given surface tension =7.5×10−2Nm−1 and g=10ms−2

The correct option is D 30 cm Self-weight of water column is to be balanced with force due to the surface tension. T(2πr)=mgT(2πr)=ρvgT(2πr)=ρAhgh=T(2πr)ρAg; h=2Tρrg

A vessel whose bottom has a round hole with diameter 0.1 mm is filled with water. The maximum height up to which water can be filled without leakage is ............. cm (given surface tension $= 7.5 \times 10^{- 2} N m^{- 1}$ and $g = 10 m s^{- 2}$

The correct option is D
30 cm

Self-weight of water column is to be balanced with force due to the surface tension.

$T (2 π r) = m g T (2 π r) = ρ v g T (2 π r) = ρ A h g h = \frac{T (2 π r)}{ρ A g}$ ; $h = \frac{2 T}{ρ r g}$