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Question

(D) The height of the water column in a capillary tube is given by the formula $h = \frac{2T \cos 	heta}{r ho g}$,where $T$ is the surface tension,

Vedclass · Accepted Answer

$\frac{R}{R-d}$

Vedclass · Answer

(D) The height of the water column in a capillary tube is given by the formula $h = \frac{2T \cos 	heta}{r ho g}$,where $T$ is the surface tension,$	heta$ is the angle of contact,$r$ is the radius of the capillary,$ho$ is the density of water,and $g$ is the acceleration due to gravity.Since $T, 	heta, r,$ and $ho$ remain constant,we have $h \propto \frac{1}{g}$.Therefore,$\frac{h_2}{h_1} = \frac{g_1}{g_2}$,where $g_1$ is the acceleration due to gravity on the Earth's surface and $g_2$ is the acceleration due to gravity at depth $d$.The acceleration due to gravity at depth $d$ is given by $g_2 = g_1 \left(1 - \frac{d}{R}ight) = g_1 \left(\frac{R-d}{R}ight)$.Substituting this into the ratio,we get $\frac{h_2}{h_1} = \frac{g_1}{g_1 \left(\frac{R-d}{R}ight)} = \frac{R}{R-d}$.Thus,the correct option is $D$.

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