The gravitational potential at a point above the surface of earth is - 5 . 12 × 10 7 J kg - 1 and the acceleration due to gravity at that point is 6 . 4 m s - 2 . Assume that the mean radius of earth to be 6400 km . The height of this point above the earth's surface is:

Step-by-step solution

Gravitational potential at a distance r from the centre of the earth is given by, V = - G M r . Therefore, we can write - G M E R E + h = - 5 . 12 × 10 7 … i also acceleration due to gravity at that point will be G M E R E + h 2 = 6 . 4 … ii By (i) and (ii), we get - G M E R E + h G M E R E + h 2 = 5 . 12 × 10 7 6 . 4 ⇒ R E + h = 80 × 10 5 m = 8000 km ⇒ h = 8000 km - 6400 km = 1600 km