# Gravitational fields MC question

Watch
Announcements
#1
Attachment 776836

How would I answer this MC question...

Q: The following data refers to two planets, P and Q.

Planet P: Radius = 8,000 km and Density = 6000 kg m^-3

Planet Q: Radius = 16,000 km and Density = 3000 kg m^-3

The gravitational field strength at the surface of P is 13.4 N kg^-1

What is the gravitational field strength of at the surface of Q?

Couldn't I just use the equation 'g = GM/r^2'

Where M could just be worked out using mass = density * vol.

It appears I don't seem to get an answer that matches to the options if I do take this approach.

So what would I do here then?

Thanks
0
2 years ago
#2
(Original post by Yatayyat)
Attachment 776836

How would I answer this MC question...

Q: The following data refers to two planets, P and Q.

Planet P: Radius = 8,000 km and Density = 6000 kg m^-3

Planet Q: Radius = 16,000 km and Density = 3000 kg m^-3

The gravitational field strength at the surface of P is 13.4 N kg^-1

What is the gravitational field strength of at the surface of Q?

Couldn't I just use the equation 'g = GM/r^2'

Where M could just be worked out using mass = density * vol.

It appears I don't seem to get an answer that matches to the options if I do take this approach.

So what would I do here then?

Thanks
I can arrive the answer as 13.4 N/kg using your method or ratio method.
0
#3
(Original post by Eimmanuel)
I can arrive the answer as 13.4 N/kg using your method or ratio method.
Oh okay, how would you use the ratio method to get the same answer? I have never heard of that method before.
0
2 years ago
#4
(Original post by Yatayyat)
Oh okay, how would you use the ratio method to get the same answer? I have never heard of that method before.

Express gravitational field strength in terms of the radius and the density, so g is directly to the product of the density and radius.
Then gQ / gP = (ρQ RQ) / (ρP RP)

If you cannot view the subscript, use a computer to view the thread.
0
#5
(Original post by Eimmanuel)
Express gravitational field strength in terms of the radius and the density, so g is directly to the product of the density and radius.
Then gQ / gP = (ρQ RQ) / (ρP RP)

If you cannot view the subscript, use a computer to view the thread.
Hmm okay, but I don’t see how ‘GM/r^2’ is equal to the density * radius?
0
#6
(Original post by Eimmanuel)
Express gravitational field strength in terms of the radius and the density, so g is directly to the product of the density and radius.
Then gQ / gP = (ρQ RQ) / (ρP RP)

If you cannot view the subscript, use a computer to view the thread.
0
2 years ago
#7
(Original post by Yatayyat)
Hmm okay, but I don’t see how ‘GM/r^2’ is equal to the density * radius?
(Original post by Yatayyat)
(Original post by Eimmanuel)
Express gravitational field strength in terms of the radius and the density, so g is directly proportional to the product of the density and radius.
Then gQ / gP = (ρQ RQ) / (ρP RP)

If you cannot view the subscript, use a computer to view the thread.

I did not say GM/r^2 is equal to the product of density and radius.

Express gravitational field strength in terms of the radius and the density.

Use mass = density × volume = ρ × (4/3)πR3

Substitute it into GM/R^2 to obtain an expression of g in terms of radius and the density.

If you cannot view the superscript, use a computer to view the thread.
0
#8
(Original post by Eimmanuel)
I did not say GM/r^2 is equal to the product of density and radius.

Express gravitational field strength in terms of the radius and the density.

Use mass = density × volume = ρ × (4/3)πR3

Substitute it into GM/R^2 to obtain an expression of g in terms of radius and the density.

If you cannot view the superscript, use a computer to view the thread.
So I get '(4G(pi)RP)/3' when g is expressed in terms of the radius and density, so how did you manage to condense it down to 'RP' when expressing the ratio, g_p / g_q = R_p * P_ p / R_q * R_ q

Thanks
0
2 years ago
#9
(Original post by Yatayyat)
So I get '(4G(pi)RP)/3' when g is expressed in terms of the radius and density, so how did you manage to condense it down to 'RP' when expressing the ratio, g_p / g_q = R_p * P_ p / R_q * R_ q

Thanks
Not sure what is “P” in “RP” as mentioned by you. I guess it to be density, ρ.

When you express g as

note that is just constant. They will not change in different planet.

You can then apply what know in mathematics known as the directly proportional relationship.

gQ = k ρQ RQ -----(1)

gP = k ρP RP -----(2)

Divide (1) by (2) or (2) by (1) to obtain a “ratio” and solve your gQ.
0
#10
(Original post by Eimmanuel)
Not sure what is “P” in “RP” as mentioned by you. I guess it to be density, ρ.

When you express g as

note that is just constant. They will not change in different planet.

You can then apply what know in mathematics known as the directly proportional relationship.

gQ = k ρQ RQ -----(1)

gP = k ρP RP -----(2)

Divide (1) by (2) or (2) by (1) to obtain a “ratio” and solve your gQ.
So essentially the constants just cancel out when you divided both expressions because the constants will always be the same?
0
2 years ago
#11
(Original post by Yatayyat)
So essentially the constants just cancel out when you divided both expressions because the constants will always be the same?
Yes.
0
#12
(Original post by Eimmanuel)
Yes.
Cheers 0
X

new posts Back
to top
Latest
My Feed

### Oops, nobody has postedin the last few hours.

Why not re-start the conversation?

see more

### See more of what you like onThe Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

### Poll

Join the discussion

#### Do you have the space and resources you need to succeed in home learning?

Yes I have everything I need (150)
60.24%
I don't have everything I need (99)
39.76%