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

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Answer & Solution

Correct Answer

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

Step-by-step Solution

Detailed explanation

Acceleration due to gravity changes with the depth,

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

\(pressure,\,P = \rho gh\)

\(Hence\,ratio,\frac{x}{y}is\left( {1 - \frac{d}{R}} \right)\)

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