# Gravitational fields MC question

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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

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

**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

0

reply

(Original post by

I can arrive the answer as 13.4 N/kg using your method or ratio method.

**Eimmanuel**)I can arrive the answer as 13.4 N/kg using your method or ratio method.

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#4

(Original post by

Oh okay, how would you use the ratio method to get the same answer? I have never heard of that method before.

**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

*g*

_{Q}/

*g*

_{P}= (

*ρ*

_{Q}

*R*

_{Q}) / (

*ρ*

_{P}

*R*

_{P})

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

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(Original post by

Express gravitational field strength in terms of the radius and the density, so

Then

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

**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

*g*_{Q}/*g*_{P}= (*ρ*_{Q}*R*_{Q}) / (*ρ*_{P}*R*_{P})If you cannot view the subscript, use a computer to view the thread.

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**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

*g*

_{Q}/

*g*

_{P}= (

*ρ*

_{Q}

*R*

_{Q}) / (

*ρ*

_{P}

*R*

_{P})

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

Hmm okay, but I don’t see how ‘GM/r^2’ is equal to the density * radius?

**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

Express gravitational field strength in terms of the radius and the density, so

Then

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

**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

*g*_{Q}/*g*_{P}= (*ρ*_{Q}*R*_{Q}) / (*ρ*_{P}*R*_{P})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)

*πR*

^{3}

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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(Original post by

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 =

Substitute it into GM/R^2 to obtain an expression of

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

**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)*πR*^{3}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

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

**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

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.

*g*

_{Q}=

*k*

*ρ*

_{Q}

*R*

_{Q}-----(1)

*g*

_{P}=

*k*

*ρ*

_{P}

*R*

_{P}-----(2)

Divide (1) by (2) or (2) by (1) to obtain a “ratio” and solve your

*g*

_{Q}.

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(Original post by

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

When you express

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.

Divide (1) by (2) or (2) by (1) to obtain a “ratio” and solve your

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

When you express

*g*asnote 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.

*g*_{Q}=*k**ρ*_{Q}*R*_{Q}-----(1)*g*_{P}=*k**ρ*_{P}*R*_{P}-----(2)Divide (1) by (2) or (2) by (1) to obtain a “ratio” and solve your

*g*_{Q}.
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#11

(Original post by

So essentially the constants just cancel out when you divided both expressions because the constants will always be the same?

**Yatayyat**)So essentially the constants just cancel out when you divided both expressions because the constants will always be the same?

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