Calculating 25% of Gravity at Height

  • Thread starter Thread starter RoughRoad
  • Start date Start date
  • Tags Tags
    Gravitation
Click For Summary

Homework Help Overview

The problem involves determining the height at which the acceleration due to gravity is reduced to 25% of its value at the Earth's surface, utilizing the gravitational formula g = GM/R².

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the application of the gravitational formula and explore the relationship between the height and the reduction in gravity. There are attempts to derive the new distance from the center of the Earth and clarify whether the height is measured from the surface or the center.

Discussion Status

Some participants have provided calculations and reasoning regarding the relationship between gravity and distance, while others have questioned the interpretation of the problem regarding the height measurement. There is acknowledgment of differing answers, and some guidance has been offered without reaching a consensus.

Contextual Notes

There is mention of a textbook answer that differs from the calculations discussed, indicating potential confusion or differing interpretations of the problem requirements.

RoughRoad
Messages
63
Reaction score
0

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

 
Physics news on Phys.org
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.
 

Similar threads

Variation of escape velocity with equal surface gravity
  • · Replies 7 ·
Replies
7
Views
1K
Gravitational Potential Energy questions near the surface of a planet
  • · Replies 8 ·
Replies
8
Views
2K
Elliptical orbit/ determine speed & potential energy
  • · Replies 1 ·
Replies
1
Views
1K
Analyzing acceleration of block on a ramp connected to a pulley
  • · Replies 15 ·
Replies
15
Views
2K
Why does the gravitational force decrease below the Earth's surface?
  • · Replies 10 ·
Replies
10
Views
4K
Oblique soccer shot calculation task
  • · Replies 38 ·
2
Replies
38
Views
4K
Circular Motion and Gravitation
  • · Replies 4 ·
Replies
4
Views
2K
Variation of potential energy with height
  • · Replies 4 ·
Replies
4
Views
3K
What is the Height of the International Space Station Above the Earth's Surface?
  • · Replies 2 ·
Replies
2
Views
4K
Work done by a force down a ramp
  • · Replies 11 ·
Replies
11
Views
2K