The approximate height from the surface of earth at which the weight of the body becomes 1 3 of its weight on the surface of earth is : [Radius of earth R = 6400 km and 3 = 1 . 732 ]

Step-by-step solution

The variation of the acceleration due to gravity with height h is given by, g ' = g 1 + h R 2 . Since the weight at given height is 1 3 of the weight at the surface ⇒ g ' = g 3 ⇒ g 1 + h R 2 = g 3 ⇒ 1 + h R = 3 ⇒ h = R 3 - 1 = 6400 × 1 . 732 - 1 = 4685   km