A body is taken from the bottom of a deep mine of depth d = R_E 2 to a height h above the surface of the earth, where R_E is the radius of the earth. If the weight of the body is found to be the same at both these locations, 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_E ) . At a depth d = R_E 2 , the value of g is: g_d = g (1 - 1 2 ) = g 2 The acceleration due to gravity at a height h (comparable to R_E ) is given by g_h = g ( R_E R_E + h )^2 . Since the weight of the body is the same at both locations, the acceleration due to gravity must be equal ( g_d = g_h ): g 2 = g ( R_E R_E + h )^2 1 2 = ( R_E R_E + h )^2 Taking the square root on both sides: 1 2 = R_E R_E + h R_E + h = 2 R_E h = ( 2 - 1)R_E Thus, t