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Gravatational Field Strength problem (Grade 12 physics)

  1. Apr 5, 2009 #1
    1. The problem statement, all variables and given/known data
    The gravitational field strength of an unknown planet is 15.5 N/kg on its surface. Calculate the value of “g” if the planets mass and radius were both doubled. Hint: Use variation.


    2. Relevant equations
    g= GM /R2


    3. The attempt at a solution

    Well my teacher gave a hint saying use variation so this was my attempt at it:

    M / 2M = R2 / 2R2

    Now this is where i kind of get stuck. If I simplify M, i am left with:

    1/2 = R2 / 2R2

    I don't now what i should do next or if i am even on the right track...

    Thanks in advanced!
     
  2. jcsd
  3. Apr 6, 2009 #2

    Hootenanny

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    Are you sure that this is correct? If you double R, how much does R2 change by?
     
  4. Apr 6, 2009 #3
    it would be 4R wouldn't it?
     
  5. Apr 6, 2009 #4

    Hootenanny

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    Indeed it would. So now you have a simple ratio question. Doubling the radius divides g by 4, doubling the mass doubles g, so the overall effect on g is ...?
     
  6. Apr 6, 2009 #5
    But how does doubling the radius dividing g by four and same with mass?


    I can see that it would be 1/2 of g or g under these conditions would be 15.5 (1/2) = 7.75 N/kg
     
  7. Apr 7, 2009 #6

    Hootenanny

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    Okay, let's take it step by step.

    You are given that the acceleration due to gravity on the surface of a planet with radius r=r0 and mass m = m0 is g=15.5 N/kg. In other words, you know that

    [tex]15.5 = \frac{Gm_0}{r_0^2}[/tex]

    Now, you are asked to determine the value of g if the radius of the planet was r=2r0 and it's mass was m=2m0. That is if both the radius and the mass are doubled. So using Newton's law of gravitation,

    [tex]\begin{aligned}
    g & = \frac{G\left(2m_0\right)}{\left(2r_0\right)^2}\\
    & = \frac{2}{4}\underbrace{\frac{G m_0}{r_0^2}}_{15.5}\\
    & = \frac{1}{2}15.5\\
    g & = 7.25 \;N/kg
    \end{aligned}[/tex]

    Do you follow?

    Correct!
    You might to recheck the final bit :wink:
     
  8. Apr 7, 2009 #7
    OHH!! That makes it muchh more clear! Thanks a bunch!
     
  9. Apr 7, 2009 #8

    Hootenanny

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    A pleasure :smile:
     
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