Can a balance give accurate reading if measured on the moon?

[alisdfd]

Question:
On the Moon, the force of gravity on an object is only about one-sixth of its value on Earth. Decide whether each of the following would give an accurate measurement of the mass if used on the Moon

a) A beam balance like the one in the diagram at the top of the page

b) A balance like the one in the photograph above. (please note the balance the question refers to is a modern type of balance- electronic one)My understanding is that a beam balance compares weight and on the moon the weight of the object changes not the mass. Since a beam balance compares weight, on the moon if an object's weight changes thus it will not be able to give the accurate reading for mass.
Therefore for (a) i said no it will not give a accurate reading for mass

However, for (b) i said yes it will give an accurate reading of mass because according to the notes i am reading from the modern type of balance detects gravitational pull but gives the reading in units of mass.

However according to the book, I was wrong.
The book answers states that (a) gives a more accurate reading of mass
(b) does not

Please can someone help me understand why?I attached a modern balance so everyone understand what type of modern balance i am talking about

 

[andrewkirk]

The beam balance works because it gives the weight by working out how many 1g disks are needed to make it balance. If the gravitational acceleration at the surface of the moon is $k\times g$ (where $g=9.8ms^{-2}$) then both the weights of the disks and of the object being weighed are multiplied by $k\times g$ instead of by $g$, so it still takes the same number of 1g disks to balance the mass as it does on Earth.

The other balance probably works with a spring or some other device that measures force, then divides the force by $g$ to estimate mass. That division is based on the assumption that the gravitational acceleration is $g$ and, since that is no correct on the moon, the estimate will be wrong.