A stone weight 100 ~N on the surface of the earth. The ratio of its weight at a height of half the radius of the earth to a depth of half the radius of the earth will be approximately

Step-by-step solution

Weight of stone at the surface of the earth, w=100 ~N At height h from the surface of earth, gravitational acceleration, g_ h = g (1+ h R )² At depth d from the surface of the earth, gravitational acceleration, g_ d =g (1- d R ) According to question, Weight at h=R / 2 Weight at d=R / 2 = m_ h ( at h=R / 2) m g_ d ( at h=R / 2) = g (1+ h R )² ( at h=R / 2) g (1- d R ) at (d=R / 2) = 1 (1+ R / 2 R )² 1- R / 2 R = 4 / 9 1 / 2 = 8 9 =0.9