The value of gravitational acceleration 'g' at a height 'h' above the earth's surface is `(g)/(4)`, then (R = __________ ) (where R = radius of the earth)

Options

A. h = R
B. `h = (R )/(2)`
C. `h=(R )/(3)`
D. `h=(R )/(4)`

Answer

A

Explanation

`g=(GM)/(R^(2))` and `g'=(GM)/((R+h)^(2))`
`therefore (g')/(g)=(1)/(4)=(GM)/((R+h)^(2))xx(R^(2))/(GM)=(R^(2))/((R+h)^(2))`
`therefore 4R^(2)=(R+h)^(2) " " therefore 2R=R+h " " h = R`