Question

At what height above the surface of earth the value of force of gravitation decreases by 10%. Radius of earth is 6400km.

Answer 1

Acceleration due to gravity is inversely proportional to square of the distance from the center of earth, therefore ratio of distance (where g will be half) to the earth's radius will be square root of 2. Thus g will be half at a distance 6.4 x 10^6 x sqrt of 2, from the center of earth.  Then height from the earth will be 6.4 x 10^6 x {sqrt of 2 )-1 } =   2.651 x 10^6 m  or 2651 km.