A vessel whose bottom has round holes with diameter `0.1 mm`, is filled with water. The maximum height up to which water can be filled without leakage is

Options

A. `100cm`
B. `75cm`
C. `50cm`
D. `30cm`

Answer

D

Explanation

For rquilibrium
Tatal upward force by surface tension
`=`Weight of the water in tube
`impliespixxDxx`surface tension (Circumference)
`=pi((D)/(2))^2xxhxx`density`xxg`(cross section)
where `rarrD`(diameter)`=0.1mm=0.01cm`
Density of water `=1xx10^-3(g)/(cm^3)`
`impliespixx(0.01)xx75`
`=pixx((0.01)/(2))^2xxhxx1xx10^-3xx1000`
`h=(75xx0.01xx4)/(0.01xx0.01)`