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Question

A vessel whose bottom has round hole with diameter of 1mm is filled with water. Only surface tension acts at hole. (Surface tension of water is 75×103 N/m and g=10m/s2). The maximum height (in cm) to which water can be filled in the vessel without leakage is:

A
2
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B
3
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C
4
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D
1
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Solution

The correct option is D 3
The vertical force due to surface tension at the whole is
(Tcosθ)L=(Tcosθ)2πr
and it would balance the weight mg of the drop
m=πr2ρh

Tcosθ(2πr)=πr2hρg
h=2Tcosθρrg

h is maximum when cosθ=1
hmax=2×75×103103×5×104×10
=0.03m
=3cm

53348_43191_ans_918772b23871476bb6a3683629376a69.png

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