# How can a beam balance measure mass?

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).

## 1 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!

• My teacher had asked in an assignment to write a device which measures weight... I wrote beam balance... she scolded me and said that beam balance measures mass not weight... I started arguing with her so I got punished... so, I was right, right? – Adik001 Mar 24 '17 at 12:32
• You are correct and she is wrong. If you carry out the experiment in water, the beam balance won't measure the mass, it will measure the net force the object applies on the beam balance (the buoyant forces will provide some lift for the object, thus, reducing the net force which the object applies on the object). There is no 'simple' device which can directly measure mass as far as I know. – Yashas Mar 24 '17 at 12:34
• I can however, think of reasons for why she said so. When we use a beam balance, the standard weights we use are written in terms of its mass (not weight). Therefore, when you take readings using a beam balance, you report the value as mass (even though it isn't really the mass). – Yashas Mar 24 '17 at 12:36