A glass capillary tube of inner diameter 0.28 | vedclass

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(D) The capillary rise $h$ is given by $h = \frac{2T}{r \rho g}$,where $T$ is surface tension,$r$ is the radius,$\rho$ is density,and $g$ is accelerat

Vedclass · Accepted Answer

$101$

Vedclass · Answer

(D) The capillary rise $h$ is given by $h = \frac{2T}{r ho g}$,where $T$ is surface tension,$r$ is the radius,$ho$ is density,and $g$ is acceleration due to gravity.To keep the water level in the capillary at the same height as the vessel,we must apply an external pressure $P$ to counteract the capillary pressure.The pressure difference across the meniscus is $\Delta P = \frac{2T}{r} = \frac{4T}{d}$,where $d$ is the diameter.Given $T = 0.07 \,N/m$ and $d = 0.28 	imes 10^{-3} \,m$,the pressure difference is $\Delta P = \frac{4 	imes 0.07}{0.28 	imes 10^{-3}} = \frac{0.28}{0.28 	imes 10^{-3}} = 10^3 \,N/m^2$.The total pressure $P$ required is $P = P_0 + \Delta P$,where $P_0 = 10^5 \,N/m^2$.$P = 10^5 + 10^3 = 100 	imes 10^3 + 1 	imes 10^3 = 101 	imes 10^3 \,N/m^2$.Thus,the value is $101$.

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