1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Value of g on Earth with a smaller radius

  1. Nov 1, 2009 #1
    What would be the value of g if the radius of the earth was decreased by half while maintaining the same mass.

    This is what I did

    g = MG / R^2

    g = MG / (0.5R)^2

    g = MG / 0.25R^2

    0.25g = MG / R^2

    I know this is not correct and the actual answer is 4g because as you get closer to the center of the Earth the gravitational force will increase but I cannot figure out why this attempt is wrong.
  2. jcsd
  3. Nov 1, 2009 #2


    User Avatar
    Science Advisor
    Homework Helper

    Hi Jimmy25! :smile:

    (try using the X2 tag just above the Reply box :wink:)
    Why did you put that 0.25 on the LHS? :confused:
  4. Nov 1, 2009 #3


    User Avatar
    Gold Member

    What you have initially is the gravitational acceleration due to the Earth while you're at the surface, or at a distance R. You then manipulated the equation to ask not what the value of g would be at the surface if the radius was half as large, but what would the value of the acceleration be at that same distance R if the radius was half as large.

    What I would do is setup a ratio, g' and g, where g' is at the surface of some planet with radius R' with the same mass, but then take R' = 0.5R and divide the two equations.
  5. Nov 1, 2009 #4
    you confuse the values of g before and after the shrinking of the earth

    you have g_old = MG/R^2

    now g_new is MG/(0.5*R)^2

    and (0.25)*g_new = MG/R^2 = g_old so

    g_new = 4*g_old, as expected
  6. Nov 1, 2009 #5
    Ok I see. So gold was equal to one quarter gnew

    Thanks, was racking my brain over this one. Sometimes the simplest question can be the most challenging.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook