Question 149 of 223

Which of the following most closely depicts the correct variation of the gravitation potential, $V(r)$ with distance $r$ due to a large planet of radius $R$ and uniform mass density? (figures are not drawn to scale)

ABCD

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Answer: (C)

At inside points $(r\lt R)$, $V=-\dfrac{GM}{2{R}^{3}}\left(3{R}^{2}-{r}^{2}\right)$. So at the centre, $r=0\Rightarrow V=-\dfrac{3}{2}\dfrac{GM}{R}$. At outside points $\left(r\gt R\right)$, $V=\dfrac{-GM}{r}$. At surface, $V=\dfrac{-GM}{R}$. So the gravitational potential is non-uniform and negative.