If the acceleration due to gravity experienced by a point mass at a height h above the surface of earth is same as that of the acceleration due to gravity at a depth α h h ≪ R e ) from the earth surface. The value of α will be _____ . (use R e = 6400 km )

Step-by-step solution

Acceleration due to gravity at a height h above the earth's surface is given by g 1 - 2 h R e And acceleration due to gravity at depth d below the earth surface is given by g 1 - d R e . As g above = g below So, g 1 - 2 h R e = g 1 - d R e ⇒ 2 h R e = d R e ⇒ α h = d Thus, the value of α = 2 .