In a certain region of space gravitational field is given by I = $-\left(\frac{k}{r}\right)$. Taking the reference point to be at $r=r_0$ with $v=v_0$, the potential (V) is given by

V = $K \log \frac{r_0}{r}+v_0$

We know that I = $-\frac{d V}{d r}$

⇒ $-\frac{k}{r}=-\frac{d V}{d r} \Rightarrow \int\limits_{v_0}^v d V = K \int\limits_{r_0}^r \frac{d r}{r}$

$\Rightarrow V=K \log \frac{r}{r_0}+v_0$