A large vessel having a very small circular hole of diameter 1 mm at the bottom is filled with water. Up to what height (in cm ) water can be filled in the vessel so that there is no leakege? [Surface tension of water =7.5 × 10-2 Nm -1 and g =10 ms -2 ]

Question

A large vessel having a very small circular hole of diameter 1 mm at the bottom is filled with water. Up to what height (in cm ) water can be filled in the vessel so that there is no leakege? [Surface tension of water =7.5 × 10-2 Nm -1 and g =10 ms -2 ] (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

Water will not leak out from the hole if the weight of water column is supported by the force due to surface tension. Using the relation,

h = \frac{2 T}{r ρ g} = \frac{2 \times 7.5 \times 1 0 ^{- 2}}{0.5 \times 1 0 ^{- 3} \times 1 0 ^{3} \times 10}

= 3 \times 1 0^{- 2} m = 3 c m

Q. A large vessel having a very small circular hole of diameter 1mm at the bottom is filled with water. Up to what height (in cm ) water can be filled in the vessel so that there is no leakege? [Surface tension of water =7.5×10−2Nm−1 and g=10ms−2 ]

Water will not leak out from the hole if the weight of water column is supported by the force due to surface tension. Using the relation, h=rρg2T​=0.5×10−3×103×102×7.5×10−2​ =3×10−2m=3cm

Q. A large vessel having a very small circular hole of diameter $1 mm$ at the bottom is filled with water. Up to what height (in $c m$ ) water can be filled in the vessel so that there is no leakege? [Surface tension of water $= 7.5 \times 1 0^{- 2} N m^{- 1}$ and $g = 10 m s^{- 2}$ ]

Water will not leak out from the hole if the weight of water column is supported by the force due to surface tension. Using the relation,
$h = \frac{2 T}{r ρ g} = \frac{2 \times 7.5 \times 1 0 ^{- 2}}{0.5 \times 1 0 ^{- 3} \times 1 0 ^{3} \times 10}$
$= 3 \times 1 0^{- 2} m = 3 c m$