Next, is this the exact statement?Deebu R said:would decrease by nearly...%
Yes, doesn't gravitation decrease to zero when we go to the core?Bystander said:Next, is this the exact statement?
I understand but if Earth shrinks then isn't it like moving towards the core?Bystander said:Yes, but we're talking about surface gravity.
What does volume have to do with it when density is not remaining constant? Post #1 already has the correct formula.Bystander said:Start with a calculation of the new volume.
As you move toward the core, you dig down, leaving a portion of the Earth above your head. The portion of the Earth that is farther from the core than you are ceases to have any net gravitational effect on you.Deebu R said:I understand but if Earth shrinks then isn't it like moving towards the core?
So if the mass remains the same gravity does not change?jbriggs444 said:What does volume have to do with it when density is not remaining constant? Post #1 already has the correct formula.
As you move toward the core, you dig down, leaving a portion of the Earth above your head. The portion of the Earth that is farther from the core than you are ceases to have any net gravitational effect on you.
If the Earth shrinks beneath your feet, the entire mass of the Earth remains beneath your feet and continues to affect you.
If you consider Newton's universal law of gravity:Deebu R said:So if the mass remains the same gravity does not change?
I got g1 - g2 =98GM/99jbriggs444 said:If you consider Newton's universal law of gravity:
##F = \frac{G m_1 m_2}{r^2}##
indeed gravity does not change. But if you want to keep your feet on the surface of the shrunken Earth than, as Bystander suggests, it is surface gravity that you need to consider. Your original post correctly considered the effect of this in reducing the r term.
Edit: The problem statement asks for a percentage decrease. What percentage decrease did you compute?
I do not understand that answer at all. Where did the 98 come from, where did the 99 come from and what are the units on that answer?Deebu R said:I got g1 - g2 =98GM/99
It makes the question "interesting".g is inversely proportional to R^2 then shouldn't gravity increase as radius decrease? So won't that make the question wrong?
So the question is wrong?Bystander said:This could be a "re-tread" problem; it "expands" one year, "contracts" the next, and the subsequent parts aren't always kept "in sync" with the rest of the statement.
Well I guess you can say it's interesting when it poses no threat. But imagine sitting in an exam hall and this shows up and you hear a voice in your head saying "your God, where is he now?"...jbriggs444 said:It makes the question "interesting".
That is incorrect. Please learn to use parentheses and decimal points.Deebu R said:g1= GM/R^2
g2= GM/ (R-R/100)^2.
Using (a-b)^2 rule
g2= GM/ 100R^2-2R^2+R^2 = GM/99R^2
Helpers won't directly confirm or deny an answer unless you show exactly how you arrived at it.Deebu R said:Is the right answer 1 percent?
Try again, M O R E S L O W L YDeebu R said:I did g1- g2 this time g2= GM/0.99R^2 and got GM-0.99GM/ 0.99R^2 = 0.01/0.99
Sure. But you need to do it right without muffing the algebra. Your problem is not the physics. It's the algebra.Deebu R said:Taking g1-g2 is the correct method?
The Earth's shrinkage is caused by a decrease in mass, which in turn is caused by a decrease in the planet's core temperature. As the core cools, it loses its ability to generate heat and the planet slowly begins to contract.
The shrinkage of the Earth leads to a decrease in its overall mass, which in turn leads to a decrease in its gravitational pull. This means that objects will weigh less on a shrunken Earth compared to its previous size.
It is unlikely that the Earth will continue to shrink in the future. Currently, the rate of shrinkage is very slow and it is estimated that the process will eventually stop as the Earth reaches a stable state.
The effects of a shrunken Earth would be noticeable but not drastic. The decrease in gravity would make it easier to move and lift objects, but it could also have negative effects such as changes in the Earth's orbit and climate.
It is highly unlikely that the shrinkage of the Earth could be reversed. The process is a natural occurrence and it would require a significant amount of energy to change the Earth's core temperature and reverse the contraction.