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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
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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#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
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
reply
(Original post by Eimmanuel)
I can arrive the answer as 13.4 N/kg using your method or ratio method.
I can arrive the answer as 13.4 N/kg using your method or ratio method.
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#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.
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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(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.
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
reply
(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.
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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reply
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#7
(Original post by Yatayyat)
Hmm okay, but I don’t see how ‘GM/r^2’ is equal to the density * radius?
Hmm okay, but I don’t see how ‘GM/r^2’ is equal to the density * radius?
(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.
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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reply
(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.
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.
Thanks
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#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
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
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.
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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
,
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.
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.
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#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?
So essentially the constants just cancel out when you divided both expressions because the constants will always be the same?
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