The height vertically above the earth's surface at which the acceleration due to gravity becomes 1 % of its value at the surface is

Step-by-step solution

The acceleration due to gravity at a height h above the surface of the earth is given by the formula g_h = g ( R R+h )^2 , where g is the acceleration due to gravity at the surface and R is the radius of the earth. Given that g_h = 1 % of g , we have g_h = 1 100 g . Substituting this into the formula: 1 100 g = g ( R R+h )^2 1 100 = ( R R+h )^2 Taking the square root on both sides: 1 10 = R R+h R + h = 10R h = 9R Answer: 9R