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A long cylindrical glass vessel has a pin hole of diameter 0.2mm at its bottom. The depth to which the vessel can be lowered vertically in a deep water batch without the water entering into the vessel is (Surface tension of water = 0.07 N/m. Acceleration due to gravity = 10 m/s²)

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21 cm

28 cm

7 cm

14 cm

answer is A.

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Detailed Solution

Given,

$diameter d = 0.2 mm \Rightarrow radius r = \frac{0.2}{2} mm = 0.1 \times 10^{- 3} m$

Water cannot enter the pinhole when the hydrostatic pressure is equal to the excess pressure.

$hρg = \frac{2 T}{r}$

$h = \frac{2 T}{gρr} = \frac{2 \times 0.07}{10^{3} \times 10 \times 0.1 \times 10^{- 3}} = 0.14 m = 14 cm$

Hence the correct answer is 14cm.

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