Moon's mass from surface gravity and finding the null gravity point

[J7]

I'm completely stumped on 2 questions I have, I'm not even sure which formula's to use, I've tried many... any help??

1) Lunar gravity at the Moon's surface is only 1/6 as strong as what we experience on Earth. Since the diameter of the Moon is about 1/4 that of the Earth, the lunar mass is about :
a) 3 x 10^-3 times the Earth's mass
b) 1 x 10^-2 times the Earth's mass
c) 3/8 the Earth's mass
d) 1/3 of the Earth's mass
e) 3 times the Earth's mass


2) At what point between the Earth, mass M_E and the Moon, mass 0.0123 M_E will their gravitational fields cancel each other (i.e. at what point willa small mass experience zero net force?)
a) at the centre of the Earth
b) At the centre of mass of this sysytem
c) at a distance 50% between the two
d) At a distance 74% of the way from the Earth to the Moon
e) none of these

Any help to set me on track would be really appreciated! Thanks

 

[arildno]

Which formulas have you tried out?

 

[J7]

Many, but i have a feeling I'm using them incorrectly, and because I'm not exactly sure of what each thing in the formulas stands for, I can't substitute in for them.

 

[arildno]

All right, please write down a single formula you think is right.
Then, describe those quantities you know what means
Don't double post; stop the thread in Gen.Physics.

 

[J7]

I figured the first one out, thanks anyway, I'm going to try the second one once more on my own