A long cylindrical glass vessel has a pinhole of diameter 0.2 mm at its bottom. The depth to which the vessel can be lowered vertically in a deep water bath without the water entering into the vessel is (surface tension of water, T=`0.07 Nm^-1`, and accleration due to gravity, `g=10 ms^-2`)

Options

A. 14 cm
B. 7 cm
C. 21 cm
D. 28 cm

Explanation

Given diameter of a pinhole d=0.2 mm
`therefore` radius of pinhole `r=0.2/2=0.1mm=0.1 times 10^-3 m`
When the hydraulic pressure is equal to the excess pressure, then water cannot enter the pinhole
Hence, `hpg=(2r)/r`
When h= depth up to which cylinder is immersed
p= density of water
and r= radius of a pinhole
`thereforeh=(2r)/(pgr)=(2 times0.07)/(10^3 times10 times 0.1 times10^-3)`
`=0.14 m=14 cm`
Hence, the depth to which the vessel can be lowered vertically in a deep water bath without the water entering into the vessel is 14 cm.