How do mass and radius affect gravitational pull on planets?

In summary, the planets have different masses and radii, but when their masses and radii are averaged out, the planets have the same gravitational force, which means that a person on Planet B would have the greatest weight.
  • #1
momoneedsphysicshelp
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Homework Statement
A 60 kg person stands on each of the following planets. On which planet is their weight the greatest?
Planet A mass M and Radius 3R
Planet B mass 2M and Radius 2R
Planet C mass 2 M and Radius 3 R
Planet D mass 3 M and Radius 3R
Relevant Equations
A) Planet A
B) Planet B
C) Planet C
D) Planet D
E) Planets B and D
F) The weight is the same on all
Can someone please verify if my reasoning is accurate?

I chose E) Planets B and D because they both have the same ratio of mass to radius which is the lowest of all the other planet options. Due to the fact that they have mass and radius evened out the gravitational pull will pull weight down more than any pf the other planets.
 
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  • #2
momoneedsphysicshelp said:
Homework Statement:: A 60 kg person stands on each of the following planets. On which planet is their weight the greatest?
Planet A mass M and Radius 3R
Planet B mass 2M and Radius 2R
Planet C mass 2 M and Radius 3 R
Planet D mass 3 M and Radius 3R
Relevant Equations:: A) Planet A
B) Planet B
C) Planet C
D) Planet D
E) Planets B and D
F) The weight is the same on all

Can someone please verify if my reasoning is accurate?

I chose E) Planets B and D because they both have the same ratio of mass to radius which is the lowest of all the other planet options. Due to the fact that they have mass and radius evened out the gravitational pull will pull weight down more than any pf the other planets.
For Comparing Weight we have to compare M/R² Not M/R As Weight= GM₁M₂/R² and G,M₂(Mass of Object) are constant so Weight ∝M/R².
 
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  • #3
Hemant said:
For Comparing Weight we have to compare M/R² Not M/R As Weight= GM₁M₂/R² and G,M₂(Mass of Object) are constant so Weight ∝M/R².
But even considering that my answer of E) Planets B and D is correct right?
 
  • #4
Does the math work for that answer ? Bluntly, just guessing isn't going to get you anywhere. Show some work.
 
  • #5
You have to compare the ratio $$\frac{M_{planet}}{R_{planet}^2}$$ for all the planets. For example for the planet A it is $$\frac{M_A}{R_A^2}=\frac{M}{(3R)^2}=\frac{1}{9}\frac{M}{R^2}$$.
 
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  • #6
Delta2 said:
You have to compare the ratio $$\frac{M_{planet}}{R_{planet}^2}$$ for all the planets. For example for the planet A it is $$\frac{M_A}{R_A^2}=\frac{M}{(3R)^2}=\frac{1}{9}\frac{M}{R^2}$$.
the answer would be B) Planet B because it has the greatest mass/radius value in comparison to the other options
 
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  • #7
Yes i also think the correct answer is Planet B. Because it has the greatest mass/(radius squared) value :D.
 
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Related to How do mass and radius affect gravitational pull on planets?

1. What is the relationship between mass and radius in planets?

The mass and radius of a planet are directly related, meaning that as the mass of a planet increases, so does its radius. This is because the force of gravity, which determines the mass of a planet, also affects its shape and size.

2. How does the mass and radius of Earth compare to other planets in our solar system?

Earth has a relatively large mass and radius compared to other planets in our solar system. It is the fifth largest planet in terms of mass and the third largest in terms of radius. However, it is much smaller than gas giants like Jupiter and Saturn.

3. Can the mass and radius of a planet change over time?

Yes, the mass and radius of a planet can change over time. This can happen through processes such as meteorite impacts, volcanic activity, and erosion. However, these changes are usually very gradual and may not be noticeable in a human lifetime.

4. How do scientists measure the mass and radius of a planet?

Scientists use various methods to measure the mass and radius of a planet. For example, they can use spacecraft to measure the gravitational pull of a planet, which can then be used to calculate its mass. They can also use telescopes to measure the size and shape of a planet, which can then be used to calculate its radius.

5. Is there a limit to how large or small a planet's mass and radius can be?

Yes, there is a limit to how large or small a planet's mass and radius can be. The smallest possible planet is about the size of our moon, while the largest possible planet is about 13 times the mass of Jupiter. This is due to the physical properties of matter and the conditions necessary for a planet to form and maintain its shape.

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