A long cylindrical glass vessel has a pinhole | vedclass

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Question

(A) Given,diameter of the pinhole,$d = 0.2 \,mm$. Radius of the pinhole,$r = d/2 = 0.1 \,mm = 0.1 	imes 10^{-3} \,m$. Water will not enter the vessel

Vedclass · Accepted Answer

$14$

Vedclass · Answer

(A) Given,diameter of the pinhole,$d = 0.2 \,mm$. Radius of the pinhole,$r = d/2 = 0.1 \,mm = 0.1 	imes 10^{-3} \,m$. Water will not enter the vessel as long as the hydrostatic pressure at the bottom is balanced by the excess pressure due to surface tension. The condition for equilibrium is $h ho g = \frac{2T}{r}$. Here,$h$ is the depth of immersion,$ho = 10^3 \,kg/m^3$ is the density of water,$T = 0.07 \,N/m$ is the surface tension,and $g = 10 \,m/s^2$. Substituting the values: $h = \frac{2T}{ho g r} = \frac{2 	imes 0.07}{10^3 	imes 10 	imes 0.1 	imes 10^{-3}}$. $h = \frac{0.14}{1} = 0.14 \,m = 14 \,cm$. Thus,the vessel can be lowered to a depth of $14 \,cm$ without water entering it.

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