Gravitational fields

The gravitational field strengths at the surfaces of the Earth and the Moon are 9.8 N kg–1 and 1.7 N kg–1 respectively. If the mass of the Earth is 81 × the mass of the Moon, what is the ratio of the radius of the Earth to the radius of the Moon?

The gravitational field strength at the surface of the Earth is 6 times its value at the surface of the Moon. The mean density of the Moon is 0.6 times the mean density of the Earth.
What is the value of the ratio ?

I need help with these questions please.

For the first part i would write expressions for gravitational field strength of earth and moon, using g=GM/r^2. Then u can divide ur expression for the moon by ur expression from the earth. That is a starting point.

Hint: the ratio can also be written as radius of earth/radius of moon

In regards to your second question what is the ratio u are meant to be calculating and is it related to the first question.

I'll try again tomorrow and check the question again. I didn't copy the second one properly but I think that that one is also meant to be to work out ratio of the radius of the earth over the radius of the moon. The questions are separate but I suppose the answers would be similar.

For the second one again consider the gravitational field strength at the surface of each body, using g=GM/r^2. However remember that each body is a sphere and so the m=density*volume. But the volume is given by 4/3*pi*r^3.

U can sub in values and reduce each equation for g at earth surafce and moon surface down, then divide them and u should be able to work out a ratio.

Let me know how u get on.

lol I got it now the answers are 3.7 and 3.6. I think I tried to rush them and didn't think clearly about it.

I got something like that when i did it.

Yeah it is I've got mark schemes and they're multiple choice. Just didn't share them before in case of someone guessing the answer without doing it properly.