# Finding True Weight with False Balance

• zorro
In summary, a body weighs 6 gms on one pan and 24 gms on the other of a false balance. The beam is horizontal when both pans are empty. The true weight of the body can be found using the basic concept of torque balance. The equations for torque balance can be written using the weights of the pans and the distance between the fulcrum and the center of mass. The result of the equations is that the true weight is the square root of 6 times 24. This balance is an "old 2 pan" balance and can measure small weights accurately.
zorro

## Homework Statement

A body weighs 6 gms when placed in one pan and 24 gms when placed on the other pan of a false balance. If the beam is horizontal when both the pans are empty, the true weight of the body is :

## The Attempt at a Solution

I don't know which concept(s) are involved.
Is it something related to 'Torque' concept ?

You only need the basic concept of torque balance.
I think the situation is like this: you place the body on one pan and some weights on the other pan such that the beam is horizontal. So the "weight" of the body = the total weight of the weights placed on the other pan.
From that, write down 2 equations for torque balance. Notice that the pans also create torques & as the question states, the beam is horizontal when the pans are empty

## Homework Statement

A body weighs 6 gms when placed in one pan and 24 gms when placed on the other pan of a false balance. If the beam is horizontal when both the pans are empty, the true weight of the body is :

## The Attempt at a Solution

I don't know which concept(s) are involved.
Is it something related to 'Torque' concept ?
In false balance,the fault may be either the weight of the pans are not equal or the fulcrum is not on the center of mass or the both. Since the pan is horizontal when both the pans are empty, both the faults must be there in the balance.
If W1 and W2 are the weighs of the pans, and W0 is the true weight of the object and x is the distance between the fulcrum and the CM, then
(W1)(l+x) = (W2)(l-x) ...(1)
(W1+6)(l+x) = (W0+W2)(l-x) ...(2)
(W1+W0)(l+x) = (24+W2)(l-x) ...(3)
Can you proceed from here on?

Is it not 6g and 7g?
What type of balance is this? Is it the 'old 2 pans' balance? If yes then how can it measure so small weight?

Is it not 6g and 7g?
What type of balance is this? Is it the 'old 2 pans' balance? If yes then how can it measure so small weight?
Yes. It is old 2 pan balance and true weight is sqrt(6*24).

## What is "Finding True Weight with False Balance"?

"Finding True Weight with False Balance" is a scientific concept that refers to the method of determining the true weight of an object by using a scale that is inaccurately calibrated or has a false balance. This technique is often used in experiments and research studies to compensate for errors in the measurement process.

## How does "Finding True Weight with False Balance" work?

The principle behind "Finding True Weight with False Balance" is based on the law of equilibrium, which states that the weight of an object is equal to the force acting on it. By using a scale with a false balance, the weight of the object can be determined by adjusting the counterweight until the scale is balanced. This counterweight then represents the true weight of the object.

## What are the benefits of using "Finding True Weight with False Balance"?

The main benefit of using "Finding True Weight with False Balance" is that it allows for more accurate measurements. By compensating for errors in the scale or measurement process, the true weight of an object can be determined with greater precision. This can be especially useful in experiments and research studies where accuracy is crucial.

## Are there any limitations to "Finding True Weight with False Balance"?

While "Finding True Weight with False Balance" can be a useful technique, it is not suitable for all types of objects and situations. It works best for objects with a known weight range and may not be as effective for objects with irregular shapes or sizes. Additionally, the accuracy of the measurement may also depend on the skill of the person using the method.

## Can "Finding True Weight with False Balance" be used in everyday life?

While it is primarily used in scientific settings, "Finding True Weight with False Balance" can also be applied in everyday life. For example, it can be used to determine the weight of small objects such as jewelry or coins. However, it may not be as practical for larger or heavier objects, where a more accurate scale would be needed.

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