First slide

Surface tension

Question

A vessel, whose bottom has round hole with diameter 0.1 mm, is filled with water. The maximum height upto which water can be filled without leakage is (Surface tension of water is 75 dyne/cm)

Moderate

A

100 cm
B

75 cm
C

50 cm
D

30 mm

Solution

For equilibrium,
Total upward force by surface tension
= Weight of the water in tube
$\Rightarrow π \times D \times Surface tension (Circumference) = π {(\frac{D}{2})}^{2} \times h \times density \times g (cross - section)$
where, $\to D (diameter) = 0.1 mm = 0.01 cm$
Density of water = $1 \times 10^{- 3} g / {cm}^{3}$
$\Rightarrow π \times (0.01) \times 75 = π \times {(\frac{0.01}{2})}^{2} \times h \times 1 \times 10^{- 3} \times 1000$
$∴ h = \frac{75 \times 0.01 \times 4}{0.01 \times 0.01} = 30 mm$

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