There is a small hole in a hollow sphere. Wat | vedclass

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Question

(B) For water to enter the sphere,the hydrostatic pressure at depth $h$ must overcome the excess pressure due to surface tension at the hole.Given:Dep

Vedclass · Accepted Answer

$0.07$

Vedclass · Answer

(B) For water to enter the sphere,the hydrostatic pressure at depth $h$ must overcome the excess pressure due to surface tension at the hole.Given:Depth $h = 40 \,cm = 0.4 \,m$Surface tension $T = 0.07 \,N/m$Density of water $ho = 1000 \,kg/m^3$Acceleration due to gravity $g = 10 \,m/s^2$Hydrostatic pressure $P = ho g h = 1000 	imes 10 	imes 0.4 = 4000 \,N/m^2$.The excess pressure across a spherical meniscus at the hole is given by $\Delta P = \frac{2T}{r}$,where $r$ is the radius of the hole.Equating the pressures:$4000 = \frac{2 	imes 0.07}{r}$$r = \frac{0.14}{4000} = 0.035 	imes 10^{-3} \,m = 0.035 \,mm$.The diameter $d = 2r = 2 	imes 0.035 \,mm = 0.07 \,mm$.Thus,the correct option is $B$.

There is a small hole in a hollow sphere. Water enters it when it is taken to a depth of $40 \,cm$ under water. The surface tension of water is $0.07 \,N/m$. The diameter of the hole is .......... $mm$.

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