Question

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 :

• A. $\left(1-\frac{d}{R}\right)$
• B. $\left(1-\frac{2d}{R}\right)$
• C. $\left(\frac{R-d}{R+d}\right)$
• D. $\left(\frac{R+d}{R-d}\right)$

Answer 1

Answer: (A)

height talances additional presence hence
$\rho g_{s}x=\rho\,g_{\text{depth}}\,y$
$g_{s}\,x=g_{s}\left(1-d/R\right)y$
$\frac{x}{y}=1-\frac{d}{R}$