there are 2 ways to measure the mass of nucleus. one is by mass spectroscopy, the other one is from nuclear reaction.
the mass spectrometer contains 2 parts. the particles first enter a constant E-field. they will be separated into different radius according to their kinetic energy by formular:
after, they will enter a region of constant B field, and the radius will further separated according to their momentum.
another way is, Particles first passed a velocity filter by perpendicular electric field and magnetic filed. then use either the electric field and magnetic field to separate them. but this method will reduced the intensity of the beam, due to the velocity filter.
the basic idea of this method is the energy conservation and binding energy will converted to kinetic energy. there are many different way to do so, but the principle is that.
one example is neutron capture by proton :
the binding energy is: