# Gravitational Potential A Level Question

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#1
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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1 year ago
#2
2V
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1 year ago
#3
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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#4
(Original post by UnknowNAlegend)
2V
the answer is 8V, but I don't know the working out
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1 year ago
#5
wtf, hold on then
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1 year ago
#6
never mind i got it
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#7
(Original post by UnknowNAlegend)
never mind i got it
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1 year ago
#8
Please DO NOT post full solutions.
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1 year ago
#9
V=-GM/r
Planet N: density=d, radius= r, , mass=m, V=4/3 * pi * r^3 = volume of N

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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1 year ago
#10
(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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#11
(Original post by UnknowNAlegend)
V=-GM/r
Planet N: density=d, radius= r, , mass=m, V=4/3 * pi * r^3 = volume of N

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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#12
(Original post by RogerOxon)
Not if it was -V on the first one.
can you elaborate on that please?
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1 year ago
#13
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.

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

1
#14
(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.

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

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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1 year ago
#15
Ok sure
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#16
(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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1 year ago
#17
Firstly list out your relevant equations for this one
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#18
(Original post by UnknowNAlegend)
Firstly list out your relevant equations for this one
V=-GM/r
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1 year ago
#19
Theres more
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1 year ago
#20
w=mV??
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