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Question on gravitation and rotation of the Earth

  1. Apr 30, 2015 #1
    1. The problem statement, all variables and given/known data
    A body is suspended on a spring balance in a ship sailing along the equator with a speed ## v' ## . If ## \omega ## is the angular speed of the earth and ## \omega_0 ## is the scale reading when the ship is at rest , the scale reading when the ship is sailing, will be very close to
    (a) ## \omega_0 ##
    (b) ## (\omega_0)(1 + \frac { 2 \omega v'}{g}) ##
    (c) ## (\omega_0)(1 \mp \frac { 2 \omega v'}{g}) ##
    (d)none of these
    2. Relevant equations
    Let mass of object be m
    Radius of earth be R.
    Tension in spring balance=Reading in spring balance = ## \omega_0 ##
    Tension be T when ship not sailing and Tension be T' when ship is sailing

    When ship is not sailing
    ## mg - T = m (\omega)^2 R ##
    When ship is sailing
    ## mg - T' = m (\omega \mp v'/R)^2 R ##
    I solved for T' but the answer is not coming.
    I could show the working but latex is hard to write.
     
  2. jcsd
  3. Apr 30, 2015 #2

    haruspex

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    But if you don't post your working nobody can tell where you are going wrong.
     
  4. Apr 30, 2015 #3
    IMG_20150501_033610.jpg
     

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  5. Apr 30, 2015 #4

    haruspex

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    That's fine so far, but notice that in the answers everything is expressed as a multiple of ##\omega_0##. Get your answer into that form. (You will probably also need to discard some third order term.)
     
  6. Apr 30, 2015 #5
    Wait a minute. Doesn't the value of g that we use account for the centripetal force due to rotation of earth? Is ## g- (\omega)^2 R =g ## using approximation? If yes then how?
     
  7. Apr 30, 2015 #6
    I got the answer. Thanks a lot.
     
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