`text((a)) text(With Altitude :)`

At the surface of the earth `g = (GM)/R^2`

For a height `h` above the surface of the earth, `g' = (GM)/(R +h)^2`

`(g')/g = R^2/(h +R)^2 = 1/(1+h/R)^2` or, `g' = g/(1+h/R)^2`

So, with increase in height g' decreases. If `h < < R ` .

`g' = g[1+ h/R]^(-2) = g[1- (2h)/R]` or `g' = g[1-(2h)/R]`

`text((b)) text(With Depth :)`

At the surface of the earth ` g= (GM)/R^2`

for a point at a depth `d` below the surface,

`g' = (GM)/R^3[R-d]` `[therefore (g')/g = ((R-d)/R)]`

i.e., `g' = g(1- d/R).......................(1)`

So with Increase in depth below the surface of the earth,g' decreasing and at the center of the earth it becomes zero.
It should be noted that value of g' decreases if we move above the surface or below the surface of the earth.


`text((c)) text(Due to Rotation of Earth :)`

The earth is rotating about its axis from west to east. So, the{fig-1}

a non inertial frame of reference. Everybody on its surface experiences a centrifugal force `m omega^2 R cos alpha .` Where `alpha` is latitude of the place. The net force on a particle on the surface of the earth

`R = sqrt(m^2g^2 +m^2omega^4R^2 cos^2 alpha +2(mg)(m omega^2R cos alpha)(cos(180-alpha))) = mg'`.............(2)

Therefore,

(i) `g'` is maximum `(=g)` , when `cos alpha =` mimimum `=0` i.e,
`alpha = 90^o` i.e, at the pole

(ii) `g'` is minimum `(= g-omega^2R)` , when `cos alpha` maximum `=1`
i.e, `alpha =0^o` , i.e.. at the equator.