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 (Surface tension of water = 75 dyne cm-1 and g = 1000 cm s-2)

Question

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 (Surface tension of water = 75 dyne cm-1 and g = 1000 cm s-2) (A) 100 cm (B) 75 cm (C) 60 cm (D) 30 cm

Tardigrade Admin · Accepted Answer

As (2T/R)=ρ gh, h=(2T/Rρ g)=(4T/Dρ g) =(4×75/0.1×10-1×103) (∵ R=D/2 and ρ=1g/per cc) or h=30 cm

Q. 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
(Surface tension of water $= 75$ dyne $c m^{- 1}$ and $g = 1000 c m s^{- 2}$ )

$100 c m$

$75 c m$

$60 c m$

$30 c m$

As $\frac{2 T}{R} = ρ g h$ ,
$h = \frac{2 T}{Rρ g} = \frac{4 T}{D ρ g}$
$= \frac{4 \times 75}{0.1 \times 1 0 ^{- 1} \times 1 0 ^{3}}$
( $∵ R = D /2$ and $ρ = 1 g /$ per $cc$ )
or $h = 30 c m$

Q. A vessel, whose bottom has round holes with diameter 0.1mm, is filled with water. The maximum height up to which water can be filled without leakage is (Surface tension of water =75 dyne cm−1 and g=1000cms−2)

100cm

75cm

60cm

30cm