If R is the radius of the Earth then the height above the Earth's surface at which the acceleration due to gravity decreases by 20 % is

Step-by-step solution

If g and g h denote the acceleration due to gravity at the Earth's surface and at the height h above the Earth's surface respectively, then g h g = R 2 ( R + h ) 2 But according to the equation g h = g - 20 100 g = 80 100 g = 4 5 g ∴ 4 5 = R 2 R + h 2 o r 4 5 = R R + h or 2 5 = R R + h o r 2 R + 2 h = 5 R or 2 h = 5 - 2 R o r h = 5 - 2 R 2 = 5 2 - 1 R