In Newtonian physics, mass is the amount of matter in an object. So, how can a beam balance measure the amount of matter in an object (which is the mass of the object).
Answer
A beam balance does not measure mass; it measures weight.
The gravitational force of attraction between the earth and an object depend on the mass of the object.
$$F = G\frac{Mm}{R^2}$$
where $G$ is the universal gravitational constant, $M$ is the mass of the earth, $m$ is the mass of the object and $R$ is the radius of the earth.
For convenience sake, we define a new quantity called acceleration due to gravity which does not depend on the mass of the object (therefore, has the same value for all the objects).
$$g = \frac{G}{M}{R^2}$$
Using the above simplification, we say:
$$F = mg$$
The beam balance measures the force $F$ exerted by the mass on the beam balance. The beam balance does not directly measure the mass. It uses the fact that the gravitational force on the object is proportional to its mass.
So what if you try to lift the object while it is being measured? You are reducing its weight, right? Does the beam balance read a smaller value?
Yes!
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