Question

Pls help in finding the gravitational potential

Answer 1

Find the potential and force on a mass m outside and inside the earth in terms of g, the acceleration due to gravity, assuming earth has uniform density and radius R


For a mass m, the potential energy of it in the gravitational field of a spherical shell of radius r' and uniform mass distribution m' is given by
γ=const. if m is inside the shell
γ=-Cm'/r if m is outside the shell, where r is the distance from the center of the sphere to the mass and C is a constant

It has the answers provided,
Outside:
F=mgR^2/r^2, γ=-mgR^2/r
Inside:
F=mgr/R, γ=mg/2R*(r^2-3R^2).

As a hint, to find the constants, when r=R, F=mg.

Answer 2

from where should i start....

Answer 3

0 to R integral -Cm'/r
for outside the shell?

Answer 4

integrating F.dr gives u potential right ?

Answer 5

yes, but F has to be found first right?

Answer 6

if i understand the q correctly,
u need to show the line integral F.dr = -Cm'/r

Answer 7

yes....

Answer 8

oh, F is not given is it ?

Answer 9

no, have to start from basic ...

Answer 10

ohk... @Vincent-Lyon.Fr

Answer 11

@eliassaab

Answer 12

Of course gravitational force has to be provided at some point in this problem.
Once you have established gravitational force using Gauss law for instance, then you work out the potential V(r) by

\(\vec g=-\vec \nabla V\)

Answer 13

i integrated 0 to R -Cm/r dx and got the equation for force and field,
what about inside the earth problem?

Answer 14

@Vincent-Lyon.Fr

Answer 15

I find
\(V_{out}(r)=-\Large \frac{g_o}{2R}\normalsize (3R^2-r^2)\)
\(V_{in}(r)=-\Large \frac{g_o R^2}{r}\)

Answer 16

how did u find that..from where did u start..

Answer 17

i just started like mass fractions will be V/Vg = r^3/rg^3