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A capillary tube is immersed vertically in water and the height of the water column is x. When this arrangement is taken into a mine of depth d, the height of the water column is y. If R is the radius of earth, the ratio $\frac{x}{y}$ is :

Option 1)
$\left ( 1-\frac{d}{R} \right )$

Option 2)
$\left ( 1-\frac{2d}{R} \right )$

Option 3)
$\left ( \frac{R-d}{R+d} \right )$

Option 4)
$\left ( \frac{R+d}{R-d} \right )$

Answers (1)

best_answer

As we have learned

Ascent Formula -

$\frac{2T\cos \Theta }{\rho gr}$

- wherein

$T- surface Tension$

$r- radius\: of\: capillary\: tube$

$\rho -liquid\: density$

$\theta - Angle\ of \ contact$

height of water column in cappilary is h $= \frac{25 \cos \theta }{\rho rg}$

For water glass interface $\theta = 0 \\ h = \frac{25 }{\rho rg}$

At the surface $h = x = \frac{25}{\rho rg_0}....(1)$

$g_0 =$ acceleration due to gravity at surface at depth d

$g = g_0 \left ( 1- \frac{d}{R} \right )$

$h' = y = \frac{25 }{\rho rg_0\left ( 1- \frac{d}{R} \right )}....(2)$

$\frac{x}{y}= 1- \frac{d}{R}$

Option 1)

$\left ( 1-\frac{d}{R} \right )$

Option 2)

$\left ( 1-\frac{2d}{R} \right )$

Option 3)

$\left ( \frac{R-d}{R+d} \right )$

Option 4)

$\left ( \frac{R+d}{R-d} \right )$

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SudhirSol

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