How do mass and radius affect gravitational pull on planets?

[momoneedsphysicshelp]

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.

 

[Frigus]

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.

 

[momoneedsphysicshelp]

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?

 

[hmmm27]

Does the math work for that answer ? Bluntly, just guessing isn't going to get you anywhere. Show some work.

 

[Delta2]

You have to compare the ratio $$\frac{M_{planet}}{R_{planet}^2}$$ for all the planets. For example for the planet A it is $$\frac{M_A}{R_A^2}=\frac{M}{(3R)^2}=\frac{1}{9}\frac{M}{R^2}$$.

 

[momoneedsphysicshelp]

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

 

[Delta2]

Yes i also think the correct answer is Planet B. Because it has the greatest mass/(radius squared) value :D.