Calculating 25% of Gravity at Height

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To determine the height at which gravity falls to 25% of its value at Earth's surface, the equation g = GM/R^2 is used. By setting the new gravitational acceleration g' to g/4, it is derived that R' (the new distance from the Earth's center) equals 2R. Since the question specifies height above the Earth's surface, the final answer is R, indicating the height is equal to the radius of the Earth. The discussion confirms the method used is correct, and the textbook answer aligns with the calculations. The problem-solving process emphasizes collaboration and validation of results.
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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

 
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RoughRoad said:

Homework Equations


g= GM/R^2

Good.

RoughRoad said:

The Attempt at a Solution


You're missing this.
 
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
 
Last edited:
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.
 
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.
 

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