In a certain region of space gravitational field is given by `I = - (k//r)`. Taking the reference point to be at `r = r_(0)`, with gravitational potential `V = V_(0)`, find the gravitational potential at distance `r`.

Explanation

We know that, the garvitational intensity is equal to the negative of gradient of potential
i.e., `I = - (dV)/(dr)`.
Here, `I = - (k)/(r )`, so `(dV)/(dr) = (k)/(r )`
or `int_(V_(0))^(V) dV = int_(r_(0))^(r) (k)/(r )` or `V - V_(0) = k log_(e) .(r )/(r_(0))`
or `V = V_(0) + k log_(e).(r )/(r_(0))`