The acceleration due to gravity at a height 'h' above the surface of earth is ' g_h '. At the depth 90 km below the earth's surface the acceleration due to gravity is also ' g_h '. The value of 'h' is

Step-by-step solution

The acceleration due to gravity at a depth d is given by: g_d = g (1 - d R ) The acceleration due to gravity at a height h (where h R ) is given by: g_h = g (1 - 2h R ) Given that the acceleration due to gravity at height h is equal to that at depth d = 90 km: g_h = g_d g (1 - 2h R ) = g (1 - d R ) 2h R = d R 2h = d h = d 2 Substituting d = 90 km: h = 90 2 = 45 km Answer: 45 km