The dependence of acceleration due to gravity `g` on the distance `r` from the centre of the earth, assumed to br a sphere of radius `R` of uniform density is as shoen in Fig. below:


The correct figure is

Options

A. `(4)`
B. `(1)`
C. `(2)`
D. `(3)`

Answer

A

Explanation

The acceleration due to gravity at a depth `d` below the surface of earth is
`g' = g (1- (d)/(R )) = g ((R - d)/(R )) = g(r )/(R )` ..(i)
where, `R - d = r =` distance of location from the centre of the earth. When `r = 0, g' = 0`.
From (i) `g' prop r`, till `r = R`, for which `g' = g`
For `r gt R, g' = (gR^(2))/((R + h)^(2)) = (gR^(2))/(r^(2))` or `g' prop (1)/(r^(2))`
Here `R + h = r`
Therefore, the variation of`g` with distance `r` from centre of earth will be as shown in figure. Thus, option (a) is correct.