The acceleration due to gravity becomes `(g/2)` where g = acceleration due to gravity on the surface of the earht at a height equal to

Options

A. `4R`
B. `(R)/(4)`
C. `2R`
D. `(R)/(2)`

Answer

B

Explanation

`g = (GM)/(R^(2)), g' = (GM)/(R+ h)^(2)`
`therefore (g)/(g') = ((R + h)/(R))^(2) = ((1) + (h)/(R))^(2)`
or `(g')/(g) = (1 + (h)/(R))^(-2) = (1 - (2h)/(R))`, when `h lt lt R`.
or `(g/2)/(g) = 1 -(2h)/(R)` or `(2h)/(R) = (1)/(2) or h = (R)/(4)`