Let A and B be the points respectively above and below the earth's surface each at a distance equal to half the radius of the earth. If the acceleration due to gravity at these points be `g_(A) and g_(B)` respectivel, them `g_(B):g_(A)`

Options

A. `1:1`
B. `9:8`
C. `8:9`
D. zero

Answer

C

Explanation

`g_(A)=(GM)/((R+(R)/(2))^(2))=(4GM)/(9R^(2))`
`g_(B) = (GMr)/(R^(3))=(GM)/(R^(3))xx(R)/(2)=(GM)/(2R^(2))`
`(g_(B))/(g_(A)) = (1)/(2)xx(9)/(4)=(9)/(8)`