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(C) For a solid sphere of radius $R$ and mass $M$ with uniform density,the gravitational potential $V(r)$ is given by:Inside the sphere $(r \le R)$: $

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(C) For a solid sphere of radius $R$ and mass $M$ with uniform density,the gravitational potential $V(r)$ is given by:Inside the sphere $(r \le R)$: $V(r) = -\frac{GM}{2R^3}(3R^2 - r^2)$. This is a parabolic variation where the potential is maximum (least negative) at the surface $(r=R)$ and minimum (most negative) at the center $(r=0)$.Outside the sphere $(r > R)$: $V(r) = -\frac{GM}{r}$. This shows an inverse variation with distance.Graph $C$ correctly shows the potential starting from a negative value at the center,increasing (becoming less negative) as $r$ increases towards $R$,and then continuing to increase towards zero as $r$ increases beyond $R$.

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

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