If the densities of the moon and the earth are related by $\rho_m / \rho_e =3/5$, and if $g_m /g_e = 1/6$, then what is $R_m /R_e$? ($g=$ acceleration due to gravity and $R=$ Radius)

  • $\begingroup$ As Rod Vance suggested, try using $$g=\frac{4}{3}\pi\rho G R.$$ $\endgroup$ – DumpsterDoofus Apr 22 '14 at 12:36
  • $\begingroup$ Comment to the post (v4): It would be good if OP (or somebody else?) could try to make the title more informative. $\endgroup$ – Qmechanic Apr 22 '14 at 20:44

You need to use Gauss's law for the inverse square field, in this case gravity. This tells you that for a spherically symmetric system:

  1. The gravitational force is always directed towards the centre of the sphere.
  2. The force at radius $r$ from the centre is given by the force owing to a point mass at the centre when that point mass equals the total, spherically-symmetrically-distributed mass enclosed in a sphere of radius $r$ centred at the centre of spherical symmetry.

Details of the reasoning can be found in my answer here. This should let you get an expression for $R_m/R_e$.

  • $\begingroup$ could this question be done using dimensions or dimensional analysis? This question is in the starting chapters of class 11, so i think think there may be some easier methods to do this?? $\endgroup$ – elle Apr 22 '14 at 8:23
  • 1
    $\begingroup$ @elle Maybe: I'm not sure what your reference is (what text are you using?). Dimensional analysis will get you candidate expressions, but you can't tell which one is correct and moreover you can't get proportionality constants from it. So, unless you're specifically being asked to guess an expression by dimensional analysis, the answer is no. $\endgroup$ – Selene Routley Apr 22 '14 at 8:29
  • $\begingroup$ yeah. thanks. i too was thinking the same but the chapter thing made think it. $\endgroup$ – elle Apr 22 '14 at 8:35

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