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


The correct figure is

Options

A. (i)
B. (ii)
C. (iii)
D. (iv)

Answer

D

Explanation

(d) 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 (4). Thus , option (d) is correct.