# Question;weights,faulty balance

• konichiwa2x
In summary, the conversation discusses a problem involving a false balance and determining the true weight of a body. By setting up equations based on the given information, it is found that the true weight of the body is 12gm.
konichiwa2x
Hi,

A body weighs 8gm when placed in one pan and 18gm when placed on the other pan of a false balkance. If the beam is horizontal when both the pans are empty, then what is the true weight of the body?

konichiwa2x said:
Hi,

A body weighs 8gm when placed in one pan and 18gm when placed on the other pan of a false balkance. If the beam is horizontal when both the pans are empty, then what is the true weight of the body?

Let the pans have mass m1 and m2. Let the body have a mass of x.

When the body is placed on pan1 one has to add 8 g. to pan 2 to balance it. When the body is placed on pan2 one has to add 18 g. to pan 1 to balance it.

I would suggest that you write out the relationship between m1, m2, x and the added masses in each weighing and solve. You won't solve for m1 and m2 but you should be able to solve for m1-m2 and x.

AM

If the beam is horizontal when both the pans are empty, doesn't that mean both the pans have equal mass?

Anway, is this what you meant?
m1 = km2
m1 + x = m2 + 8
m2 + 18 = m2 + x

solving, x = 13? Is this correct?

My book says the correct answer is 12gm..

konichiwa2x said:
If the beam is horizontal when both the pans are empty, doesn't that mean both the pans have equal mass?
Not quite, because it is a false balance. But I think I may have misled you a little on my first answer.

A balance works by equalizing torque. You can say that m1r1 = m2r2 where r1 and r2 are the distances of m1 and m2 from the fulcrum. If r1 and r2 are equal, the balance balances only if m1 = m2. We are told that this is not the case here. So all we can say is that:

m1r1 = m2r2

Therefore,

(m1 + x)r1 = (m2 + 8)r2

(m1 + 18)r1 = (m2 + x)r2

Work that out for x. The answer in the book is correct.

AM

Arnab
ok thanks a lot!

## 1. What is the purpose of using weights with a faulty balance?

The purpose of using weights with a faulty balance is to determine the extent of the faultiness of the balance. By comparing the weight readings on the faulty balance with the known weights, the accuracy and reliability of the balance can be assessed.

## 2. How do you determine the accuracy of the faulty balance using weights?

To determine the accuracy of the faulty balance, you need to weigh a set of known weights on the balance and compare the readings with the actual weights. If the readings are consistently off by a certain amount, it indicates a systematic error in the balance. If the readings vary widely, it indicates random errors.

## 3. Can weights be used to calibrate a faulty balance?

Yes, weights can be used to calibrate a faulty balance. By adjusting the balance's calibration screws or weights, the readings can be made more accurate and reliable. However, if the balance is severely faulty, it may not be able to be calibrated and will need to be replaced.

## 4. What are some common causes of a faulty balance?

A faulty balance can be caused by various factors, such as wear and tear of the balance components, incorrect use or handling of the balance, and environmental factors like temperature and humidity. Inaccurate or inconsistent readings are also common signs of a faulty balance.

## 5. How can you prevent a balance from becoming faulty?

Regular maintenance and proper use and handling of the balance can prevent it from becoming faulty. It is important to clean the balance after each use, avoid overloading it, and handle it with care. Regular calibration and adjustments can also help maintain the accuracy and reliability of the balance.

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