Gravitational Field Intensity

NCERT Class 11, Chapter 8 (Gravitation) defines gravitational field intensity as the force per unit mass, $E=\frac{GM}{r^2}$, which outside a uniform sphere behaves exactly as if all mass were concentrated at the centre. At the surface, $r=R$, the field equals $g=\frac{GM}{R^2}$. At a distance $r=2R$ from the centre, $E=\frac{GM}{(2R{)}^2}=\frac{GM}{4R^2}=\frac{g}{4}$. The point lies outside the planet, so the inverse-square law applies and only the radius matters. The option $g/2$ uses a linear distance dependence instead of squaring. The option $2g$ wrongly increases the field with distance. The option $g$ ignores any change with position. As a plausibility check, doubling the distance from the centre must weaken the field by a factor of four because of the inverse-square dependence, giving $g/4$, which is smaller than the surface value as expected.