The radius of earth is R and acceleration due to gravity on its surface is g . The height at which the acceleration due to gravity becomes g 8 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' = 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' = g 8 , we substitute this into the equation: g 8 = g ( R R+h )² Dividing both sides by g gives: 1 8 = ( R R+h )² Taking the square root of both sides: 1 2 2 = R R+h Rearranging the terms to solve for h : R + h = 2 2 R h = 2 2 R - R h = (2 2 - 1) R Answer: (2 2 -1) R