Calculating 25% of Gravity at Height

[RoughRoad]

Homework Statement

At what height will the acceleration due to gravity will fall to 25% that of the Earth's surface?

Homework Equations

g= GM/R^2

The Attempt at a Solution

 

[rock.freak667]

Homework Equations

g= GM/R^2

Good.

The Attempt at a Solution

You're missing this.

 

[rajatgl16]

g=GM/R^2 or R^2=GM/g..
let g' be new value of g which is fall in 25%..
therefore 25g/100= g' or g'=g/4

R' be the new distance from surface of Earth than,

R'^2=GM/g'

as g'=g/4 therefore

R'^2=4GM/g

as GM/g= R^2 therefore R'^2=4R^2

R'^2= (2R)^2

R' = 2R


therefore answer is 'R' above surface of earth. As 2R is distance from center

 

[rock.freak667]

Since they asked for the 'height' I would assume they want from the surface and not the distance from the center.

But your method is correct.

 

[RoughRoad]

The answer given in my textbook is R. And I have worked it out with my friend and now I got the answer. But thanks to both of you for helping me solve this problem.