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Question;weights,faulty balance

  1. Oct 25, 2006 #1
    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?

    How do I do this? Please help.
     
  2. jcsd
  3. Oct 25, 2006 #2

    Andrew Mason

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    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
     
  4. Oct 25, 2006 #3
    If the beam is horizontal when both the pans are empty, doesnt 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..
     
  5. Oct 25, 2006 #4

    Andrew Mason

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    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
     
  6. Oct 26, 2006 #5
    ok thanks a lot!:smile:
     
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