Q. In a certain region of space, the gravitational field is given by $–k/r$, where $r$ is the distance and $k$ is a constant. If the gravitational potential at $r = r_{0}$ be $V_{0}$, then what is the expression for the gravitational potential V?
A) $k\log{(r/r_{0})}$
B) $k\log{(r_{0}{/r}_{\ })}$
C) $V_{0}\mathbf{+}k\log{(r/r_{0})}$
D) $V_{0} + k\log{(r_{0}/r_{\ })}$
Explanation
(c) Here, $I = \frac{dV}{dr} = - k/r$
or $dV = k\frac{dr}{r}$
Integrating it, we get
$\int_{V_{0}}^{v}{dV = \int_{r_{0}}^{r}{k\frac{dr}{r}}}$
or $V = V_{0} + k\log{r/r_{0}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.