Yatayyat
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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
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Eimmanuel
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(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.
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Yatayyat
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(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.
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Eimmanuel
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(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.
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Yatayyat
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(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?
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Yatayyat
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(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.
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Eimmanuel
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(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)
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(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.
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Yatayyat
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(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

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Eimmanuel
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(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

 g = \frac{4}{3} G \pi \rho R ,

note that  \frac{4}{3} G \pi  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.
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Yatayyat
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(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


 g = \frac{4}{3} G \pi \rho R ,


note that  \frac{4}{3} G \pi  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?
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Eimmanuel
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(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.
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Yatayyat
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(Original post by Eimmanuel)
Yes.
Cheers
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