So did I. I thought the question was whether the balance-beam would work
the same on the moon as on the earth.
1) No balance-beam is going to work if somebody has a black-hole-on-a-stick
(several jillion kg) and starts waving it around in the vicinity. Duh.
2a) As a less-pathological example, consider ye olde centrifuge. In the
cabin thereof, things are subjected to several Gees. The gradients are on
the order of a few percent per meter, thousands of times larger than the
gradients of the earth's field. It might make an innnnnteresting
assignment: devise a laboratory-grade instrument to measure mass in such
an environment.
2b) Things get even more innnnnteresting if the local g vector is
time-dependent.
3) At the opposite extreme, a much less difficult assignment: devise a
laboratory-grade instrument to measure mass in the zero-Gee environment of
a space ship.
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Note: The word "innnnnteresting" comes from an ancient Chinese curse. You
have to pronounce it with the appropriate accent.....