Water rises up to height ' x ' in a capillary tube immersed vertically in water. When the whole arrangement is taken to a depth ' d ' in a mine, the water level rises up to height Y . If R is the radius of the earth then the ratio Y : x is

Step-by-step solution

The capillary rise x at Earth's surface follows x = 2T g r with gravitational acceleration g . At depth d , gravity becomes g' = g(1 - d R ) , yielding a new rise height Y = 2T g' r . Substituting g' gives Y = 2T g r (1 - d R ) . The ratio simplifies as: Y x = 1 1 - d R = R R-d Thus Y:x = R:(R-d) , corresponding to option B .