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# Gravity, Balance and some doubts

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Nassar posted: “I have no explanation why did the scale get balanced when there are twe equal masses on both sides ???
Here is the problem:

Suppose that a have a scale and I put 1kg on one side , so this side will get down – no problem with that-

but,

if I put another 1kg but on the other side of the scale…now imagine this,
the first 1kg was down and at this very moment ( I mean before the scales started to get balanced) the new 1kg will be at top , now according to the law of Gravity , the gravitaional force affecting the lower mass is greater than that affecting the top mass (I mean the mass at the bottom is closer to the center of the earth)…
Here is my question:
What force make the mass at the buttom to rise up against the gravity???
All explanations said that its in order to equalaze the gravitational force on both sides , but this makes no sense,

First why to equalize? ,

and second ,

What force make the mass at the bottom to rise ?

For me it is not silly question..
Thank you

This is the type of doubt which we expect from students and visitors. The doubts which we encounter when we think on what we learn.

First of all let us talk about the force of gravity and its variation with position.

When we consider a metre scale balanced at a pivot, a small change in vertical height does not make much difference in force of gravity as the distance from the centre of earth to surface is 6400 kilometer but the difference in height of the two masses is only a few centimeters.

So, the force on the two masses (if they are equal) is practically the same.

Now, what make the scale get balanced horizontally?

If the scale is uniform and is balanced exactly at the centre of gravity, Then when a mass is kept on one side, it tends to turn due to the moment of force it creates. (Moment of force is the product of force and the perpendicular distance between the line of action of force and the axis of rotation). If the mass is kept on left side, it will create an anticlockwise moment.

When the second mass is kept on the other side, it creates a clockwise moment. If the two masses are equal and are kept at equal distance from the CG, the two moments will be equal and opposite.  So they balance each other.

Now, to answer why the lowered mass rises up when the second mass is placed on the other side. (I think this is the most troubling question you had)

A system is most stable when the Center of gravity is at the lower most position. Any system will tend to attain the most stable position. The system in our discussion is most stable when the scale is horizontal (with equal masses hung at equal distances).

Now, there is some more point here.

The scale will be horizontal even if we use strings of different length to suspend the masses.  (The mass of string must be negligible).It doesn’t matter How long the string is, but where on the scale is it tied. Think WHY?

The scale can be balanced horizontally with unequal masses if it is kept at a point other than the CG.

The scale can be balanced just by using a single mass when it is kept at a point  other than the CG. Here the weight of the scale itself creates the moment.

Think on …..

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