The height ‘ h ’ at which the weight of a body will be the same as that at the same depth ‘h’ from the surface of the earth is (Radius of the earth is R and effect of the rotation of the earth is neglected)

Step-by-step solution

GM ( R + h ) 2 = GM R 3 ( R - h ) R 3 = ( R + h ) 2 ( R - h ) = R 2 + h 2 + 2 hR ( R - h ) R 3 = R 3 + h 2 R + 2 hR 2 - R 2 h - h 3 - 2 h 2 R h 3 + h 2 ( 2 R - R ) - R 2 h = 0 h 3 + h 2 R - R 2 h = 0 h 2 + hR - R 2 = 0 h = - R ± R 2 + 4 ( 1 ) R 2 2 = - R + 5 R 2 = ( 5 - 1 ) 2 R