If one assume that the gravitational force due to the earth decreases in proportion to the iverse squre of the distance from the centre of the earth then which fo the followng relation between `a_(m) r_(m)` g and `R_(E)`

Options

A. `(g)/(a_(m))=(R_(m))/(R_(E ))`
B. `(g)/(a_(m))=((R_(m))/R_(E ))^(2)`
C. `(g)/(a_(m))=((R_(E))/R_(m))^(-2)`
D. both b and c

Answer

D

Explanation

Since `a_(m) prop (1)/(R_(m)^(2))`
`g prop (1)/(R_(E )^(2))`
from Eqs I and ii we get
`(g)_(a_(m))=(R_(m)^(2))/(R_(E )^(2))=(R_(E)^(-2))/(R_(m)^(-2))`