State whether the following statements are true or false:
$(a)$ The value of '$g$' is slightly less at the poles than at the equator.
$(b)$ The unit $\text{Newton/kilogram}$ $(N/kg)$ is also a unit of acceleration due to gravity.
$(c)$ The escape velocity $v_e$ for a stationary object on the surface of a planet is directly proportional to the mass and radius of the planet.

(B) False. The Earth is flattened at the poles and bulges at the equator. The radius at the poles is smaller than at the equator. Since $g = GM/R^2$,$g$ is greater at the poles than at the equator.
$(b)$ True. Since $F = mg$,$g = F/m$. The unit of force is $\text{Newton}$ $(N)$ and mass is $\text{kilogram}$ $(kg)$,so the unit of $g$ is $N/kg$,which is equivalent to $m/s^2$.
$(c)$ False. The formula for escape velocity is $v_e = \sqrt{2GM/R}$. Thus,$v_e$ is directly proportional to the square root of the mass $(\sqrt{M})$ and inversely proportional to the square root of the radius $(1/\sqrt{R})$.