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




The correct figure is

Options

A. -4
B. -1
C. -2
D. `-3`

Answer

A

Explanation

The acceleration due to gravity at the depth `d` below surface of earth is given by
`g'=(GM)/(R^(2))(1-d/R)=g(1-d/R)`
`g'=0` at `d=R`
[valud of `g` at centre of earth is equal to zero]
Thus, the variation in value of `g` with `r` is
For `r gt R`
`g'=g/((1+h/R)^(2))=(gR^(2))/(r^(2))impliesg' prop1/(r^(2))`
Here `R+h=r`
for `r lt R,g'=g(1-d/R)=(gr)/R`
Here `R-d=rimpliesg'propr `
Therefore, the variation of `g` with distance from centre of the earth will be as shown in the graph.