rotational-dynamicsstabilitystaticstorque
I'm talking about a Weighing Balance shown in the figure:
Press & Hold on onside of the horizontal beam and then release it. It makes some oscillations and comes back to equilibrium like shown in the figure.
Both the pans are of equal equal masses. When the horizontal beam is tilted by an angle using external force, the torque due to these pan weights are equal in magnitude & opposite in direction. Then why does it come back to it position? What's making it to come back?
Suppose you have a balance that looks like this:
where $m_1$ and $m_2$ are the weights you're comparing and $M$ is some large weight fixed to the balance. For simplicity let's $m_1$ is zero, so one one end of your scales you have some weight $m_2$ and there is nothing else on the other end.
You are quite correct that with simple lever scales the lever would tip over until it was vertical with $m_2$ at the bottom. However the scales pictured above would rotate only a small distance because the restoring force from the large weight $M$ would balance out the tilting force from $m_2$. The result is that the angle increases as you increase $m_2$, just as you observe in practice.
You can work out the angle of rotation just by taking moments around the pivot point, and you get:
$$ m_2gl\cos\theta = Mgh\sin\theta $$
or
$$ \tan\theta = \frac{m_2 l}{Mh} $$
up to about 25$^\circ$ $tan(\theta)$ is approximately proportional to $\theta$ so you get:
$$ \theta \propto m_2 $$
i.e. for angles less then 25$^\circ$ the angle of tilt is proprotional to the weight on the scales.
On a well designed balance scale, the center of gravity of the beam or lever arm will be just slightly below the center pivot point.
If the beam is not level, the center of gravity will be to one side or the other of the pivot, and will thus create torque as it tries to move directly below the pivot point.
The distance between the pivot point and the center of gravity of the beam will determine the scale's sensitivity, ie.. the closer the CG is to the pivot, the less torque it will apply when it is out of alignment, and the smaller the difference the scale will be able to detect.
There are no springs, or magnets that cause this effect, just gravity at work.
Best Answer
If it would only be the weights exerting torque, the balance would be in equilibrium at all angles. What makes the balance go back to the horizontal position is the fact, that the center of mass is below the beam. consider this picture
The needle exerts a torque too, so you have more torque on the side, where the plate is higher. You can have more subtle configurations (like in your picture, where the beam is rounded below) but the mechanism is the same.