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.

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(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 $(1/\sqrt{R})$.

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