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. 1
B. 2
C. 3
D. 4

Answer

D

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 g'=0
from (i) , `g prop r `till R=r for which g '=g
for `r gt 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) .