The height in terms of radius of the earth (R) , at which the acceleration due to gravity becomes g 9 , where g is acceleration due to gravity on earth's surface, is ______.

Step-by-step solution

The acceleration due to gravity at a height h above the surface of the earth is given by g' = g (1 + h R )^2 Given that g' = g 9 , we get g 9 = g (1 + h R )^2 (1 + h R )^2 = 9 1 + h R = 3 h R = 2 h = 2R Answer: 2R