Gravitational Potential A Level Question

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I-ZAAA
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Planet N has a gravitational potential –V at its surface. Planet M has double the density and double the radius of planet N. Both planets are spherical and have uniform density.

What is the gravitational potential at the surface of planet M?

I am actually clueless, can anyone help me please?
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UnknowNAlegend
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2V
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UnknowNAlegend
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radius= 2r so V=-GM/r so V/2
2* density so over the volume its 2V. Since it has 2R, volume increases by 2 and leads to potential = 4V
4/2= 2V
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I-ZAAA
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(Original post by UnknowNAlegend)
2V
the answer is 8V, but I don't know the working out
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UnknowNAlegend
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wtf, hold on then
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UnknowNAlegend
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never mind i got it
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I-ZAAA
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(Original post by UnknowNAlegend)
never mind i got it
could you please explain your working out ?
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RogerOxon
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Please DO NOT post full solutions.
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UnknowNAlegend
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V=-GM/r
Planet N: density=d, radius= r, , mass=m, V=4/3 * pi * r^3 = volume of N

PlanetM: radius= 2r,
mass= density * volume
density=2d, volume= 4/3 *pi* (2r)^3= 4/3*pi* 8r^3= 8* volume of N
Mass= 2*8= 16m
Potential, V=-GM/r=16/2= 8V
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RogerOxon
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(Original post by I-ZAAA)
the answer is 8V, but I don't know the working out
Not if it was -V on the first one.
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I-ZAAA
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(Original post by UnknowNAlegend)
V=-GM/r
Planet N: density=d, radius= r, , mass=m, V=4/3 * pi * r^3 = volume of N

PlanetM: radius= 2r,
mass= density * volume
density=2d, volume= 4/3 *pi* (2r)^3= 4/3*pi* 8r^3= 8* volume of N
Mass= 2*8= 16m
Potential, V=-GM/r=16/2= 8V
Ahh! That was clever, I never thought about the 4/3 *pi* bit. Thanks!
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I-ZAAA
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(Original post by RogerOxon)
Not if it was -V on the first one.
can you elaborate on that please?
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UnknowNAlegend
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Basically, Potential= -GM/r
For planet N, it has a radius, a density, a mass and a volume which I have labelled as letters for short.

For Planet M, the radius is twice of N's radius.
To find out M's mass, do volume* density
You're told M has two times density of N.
To find out volume of M, do 4/3*pi*r^3, however, this time, your radius is 2r since M is twice of radius of N. This results in 8 times the volume
Mass of N = 8*2=16 due to mass=density *volume
Sub in the mass and radius into V= -GM/r

soz about the calculations, only read your comment later lol
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I-ZAAA
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(Original post by UnknowNAlegend)
Basically, Potential= -GM/r
For planet N, it has a radius, a density, a mass and a volume which I have labelled as letters for short.

For Planet M, the radius is twice of N's radius.
To find out M's mass, do volume* density
You're told M has two times density of N.
To find out volume of M, do 4/3*pi*r^3, however, this time, your radius is 2r since M is twice of radius of N. This results in 8 times the volume
Mass of N = 8*2=16 due to mass=density *volume
Sub in the mass and radius into V= -GM/r

soz about the calculations, only read your comment later lol
Yeah it makes much more sense. Thanks! Mind helping me with one question? This time give me hint instead of the full answer please.
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UnknowNAlegend
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Ok sure
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I-ZAAA
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(Original post by UnknowNAlegend)
Ok sure
Thanks. This is the question:

A spacecraft of mass 1.0 × 106 kg is in orbit around the Sun at a radius of 1.1 × 1011 m

The spacecraft moves into a new orbit of radius 2.5 × 1011 m around the Sun.

What is the total change in gravitational potential energy of the spacecraft?
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UnknowNAlegend
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Firstly list out your relevant equations for this one
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I-ZAAA
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#18
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(Original post by UnknowNAlegend)
Firstly list out your relevant equations for this one
V=-GM/r
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UnknowNAlegend
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#19
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Theres more
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UnknowNAlegend
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#20
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#20
w=mV??
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