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Uncertainty question

  1. Oct 2, 2015 #1
    1. The problem statement, all variables and given/known data
    image.jpg

    2. Relevant equations
    Absolute uncertainty in θ = δθ/θ

    3. The attempt at a solution
    I know that smaller θ gives smaller actual uncertainty, thus leaving B and D out. The answer is C. but what about option A?
     
  2. jcsd
  3. Oct 2, 2015 #2

    haruspex

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    Your relevant equation is wrong.
    If the fractional error in X is r, how large is the actual error in X? How large then is the actual error in theta?
     
  4. Oct 4, 2015 #3
    The actual error in X would be rX? And rθ?
     
  5. Oct 4, 2015 #4

    haruspex

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    Yes. So what is the fractional error in theta?
     
  6. Oct 4, 2015 #5
    r ?
     
  7. Oct 4, 2015 #6

    haruspex

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    Right. Can you now see why A is wrong?
     
  8. Oct 4, 2015 #7
    No ..sorry..
    If actual uncertainty in θ is r, then the percentage uncertainty of θ would be r x100 right? Isn't the effect the same?
     
  9. Oct 5, 2015 #8

    haruspex

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    No, the percentage uncertainty is 100x fractional uncertainty.
     
  10. Oct 5, 2015 #9
    What's the difference between fractional uncertainty and fractional error?
     
  11. Oct 5, 2015 #10

    haruspex

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    Sorry, I didn't notice I had switched from uncertainty to error. For the purposes of this question it makes no difference.
    So in your post #5, you have that if the fractional (or percentage) uncertainty in x is r then the fractional (or percentage) uncertainty in theta is r.
    Can you see how that conflicts with A?
     
  12. Oct 5, 2015 #11
    Ohhhh...is it because the percentage uncertainty would be the same for all values of θ, but the uncertainty itself varies?
     
  13. Oct 5, 2015 #12

    haruspex

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    Yes.
     
  14. Oct 5, 2015 #13
    Thanks
     
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