In a certain region of space gravitational field is given by $E = \frac {-K}{r}$ where $'r'$ is the distance from a fixed point and $K$ is constant. Taking reference point to be at $r = r_0$ with $V = V_0$ the potential at a distance $r$ is

- A
$V = - {V_0} + K\,\log \,\left( {\frac{r}{{{r_0}}}} \right)$

- B
$V = {V_0} + K\,\log \,\left( {\frac{r}{{{r_0}}}} \right)$

- C
$V = + {V_0} + K\,\log \,\left( {\frac{{{r_0}}}{r}} \right)$

- D
None of these

A spherically symmetric gravitational system of particles has a mass density $\rho=\left\{\begin{array}{ll}\rho_0 & \text { for } r \leq R \\ 0 & \text { for } r>R\end{array}\right.$ where $\rho_0$ is a constant. A test mass can undergo circular motion under the influence of the gravitational field of particles. Its speed V as a function of distance $r(0 < r < \infty)$ from the centre of the system is represented by

Two heavy spheres each of mass $100 \;kg$ and radius $0.10\; m$ are placed $1.0\; m$ apart on a horizontal table. What is the gravitational force and potential at the mid point of the line joining the centres of the spheres? Is an object placed at that point in equilibrium? If so, is the equilibrium stable or unstable?

If $V$ is the gravitational potential due to sphere of uniform density on it's surface, then it's value at the center of sphere will be:-

- [JEE MAIN 2023]

At some point the gravitational potential and also the gravitational field due to earth is zero. The point is

By which curve will the variation of gravitational potential of a hollow sphere of radius $R$ with distance be depicted