Suppose the mass of the Earth were doubled (Physics 12)

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Homework Help Overview

The problem involves a hypothetical scenario where the mass of the Earth is doubled while maintaining its density and spherical shape. Participants are discussing how this change would affect the weight of objects at the Earth's surface.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants explore the implications of doubling the Earth's mass and question how the radius would change under the condition of constant density. There is a discussion about the relationship between mass, volume, and radius for a sphere.

Discussion Status

The discussion is active, with participants raising questions about the calculations and relationships involved. Some guidance has been offered regarding the relationship between mass and volume, but there is no explicit consensus on the correct approach to the problem.

Contextual Notes

One participant notes confusion regarding the calculations and references a textbook answer that differs from their own. There is also mention of an online solution that uses equations not covered in their coursework.

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Homework Statement


Suppose the mass of the Earth were doubled , but it kept the same density and spherical shape. How would the weight of objects at the Earh's surface change?


Homework Equations


Fg=Gm1m2/r^2


The Attempt at a Solution


g=G2m/r^2
g=19.59817612

g/g(on Earth - 9.8)
=2

I know this is wrong because the textbook says the answer is 1.26 or 2^1/3.
I have no idea how to get this answer. I did find an online solution but they used equations that I have not been taught.

Here is a link to the online solution:
http://archives.evergreen.edu/webpages/curricular/2005-2006/PhyAstro/0506/HW/G6solns.pdf

If anyone can explain how to get this answer step by step that would be great.
 
Physics news on Phys.org
If you double the mass, but keep the same density, what happens to the radius?
 
It would increase?
 
Did you increase the radius in your calculation?
 
No I didn't. So it would double as well?
 
Would it?
What is the relationship between mass and volume? volume and radius for a sphere?
 
I get it now. My Physics teacher explained it to me after school. Thank you!
 
Cool. Of course it would have been better if you'd reasoned it out yourself.
If you posted the answer here, you'd help someone else stuck on the same problem...?
 

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