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

Step-by-step solution

On the surface of the earth T= r h g 2 for water h= 2 T r g At a depth d , the value of acceleration due to gravity changes to g^ =g (1- d R ) , therefore g^ =g (1- d R ) , therefore aligned & h^ = 2 T r g^ d = 2 T r g (1- d R ) & h h^ = 2 T r g r g (1- d R ) 2 T =1- d R aligned