JEE Mains · Physics · STD 11 - 9.2 surface tension
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 & 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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