Question

At what depth from the surface of earth 'g' is halved

Answer 1

Gravitational force = F
Mass of earth = M
Mass of object = m
Gravitational acceleration = g
Gravitational constant = G

Radius of Earth = R
F = mg …………… eqn. 1
F = (GMm)/ R^2 … eqn. 2
equating 1 & 2
g = (GM)/ R^2

as “g” is halved put g = g/2 , new radius = r
(g/2) = (GM)/(2*R^2)

this means g is inversely proportional to distance between two masses

g = c/ (2*R^2) , where c = GM
i.e. r = R*( square root of 2 )

r = 1.4142 times of Radius of Earth is the distance where g becomes g/2