Water rises upto a height x in capillary tube immersed vertically in water . When this whole arrangement is taken to a depth d in a mine , the water level rises upto a height y . If R is the radius of the earth , then the ration `x/y` is given by

Options

A. `1+d/R`
B. `1-d/R`
C. `(R+d)/(R-d)`
D. `(R-d)/(R+d)`

Answer

B

Explanation

On the surface of the earth `T = (rhrhog)/2 ` for water
` :. h = xx = (2T)/(rrhog)`
At a depth (d),
` h = y = (2T)/(rrhog_(d)) = (2T)/(rrhog(1-d/R))`
` [ :' g_(d) = g (1-d/R) ]`
` :. x/y = (2T)/(rrhog) xx(rrhog(1-d/R))/(2T) = 1 - d/R `