# Here g=GM/R*R at the centre of earth R=0 ; M=0 why g=0 but this is in 0/0 form

1
by rahulkumar95

2015-02-15T15:07:16+05:30

### This Is a Certified Answer

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
Me = 4/3 π Re³  * d,   where  Re = Radius of Earth
Me = Mass of EArth         d = density of Earth  (we assume it is uniform)

Let us find the gravity at a distance r from the center of Earth.  Mass of Earth enclosed inside the radius r is :

M = 4/3 π r³ d  = 4/3 π r³ (3Me /Re³ 4π)
= Me r³/ Re³

Gravity at a location r distance away from center of Earth is = G (Me r³/Re³) / r²
Thus  g' = G Me r / Re³ = g r /Re ,
where g = acceleration due to gravity at the surface of Earth.

Thus  if r = 0,  g' = 0.

In other words,  M  varies as cube of R  and  in the denominator, we have a square of R.  Thus g is proportional to R inside the Earth's surface.