At what distance from the centre of the earth, the value of acceleration due to gravity g will be half that on the surface ( R = radius of earth)

Options

A. 1.414R
B. R
C. 0.414R
D. 2R

Answer

A

Explanation

`(g')/(g)=((R )/(R+h))^(2) " " therefore (1)/(2)=((R )/(R+h))^(2)`
`therefore (1)/(sqrt(2))=(R )/(R+h)`
`therefore (R+h)=sqrt(2)R = 1.414 R`
`therefore` The distance `= 1.414 R`