The gravitational potential $\mathrm{V}$ at a point $\mathrm{P}$ lying outside a solid sphere is given by: $\mathrm{V}=-\mathrm{GM}/\mathrm{x},$ where $\mathrm{G}$ is gravitational constant, $\mathrm{M}$ is the mass of sphere and $\mathrm{x} \mathrm{is}:$

If $\mathrm{g}$ is acceleration due to gravity on the earth's surface, the gain in the potential energy of an object of mass $\mathrm{m}$ raised from the surface of the earth to a height equal to the radius $\mathrm{R}$ of the earth, is :

A body enters the gravitational field of the earth from external atmosphere. The potential energy of the earth body system:

Two satellites are revolving in the same circular orbit. Their :

Two satellite of masses ${\mathrm{m}}_1 \mathrm{and} {\mathrm{m}}_2 \left({\mathrm{m}}_1>{\mathrm{m}}_2\right)$ are revolving round the earth in circular orbit of radii ${\mathrm{r}}_1 \mathrm{and} {\mathrm{r}}_2 \left({\mathrm{r}}_1>{\mathrm{r}}_2\right)$ respectively. Which of the following statement is true regarding their speeds ${\mathrm{v}}_1 \mathrm{and} {\mathrm{v}}_2 ?$

Two satellite $\mathrm{A} \mathrm{and} \mathrm{B}$ round a planet $\mathrm{P}$ in circular orbits having radii $4\mathrm{R} \mathrm{and} \mathrm{R}$ respectively. If the speed of the satellite $\mathrm{A} \mathrm{is} 3\mathrm{v},$ the speed of satellite $\mathrm{B}$ will be :

A spherically symmetric gravitational system of particles has a mass density

                                                               $$\begin{gathered} \mathrm{\rho }=\left\{{\mathrm{\rho }}_{\mathrm{o}} \mathrm{for} \mathrm{r}⩽\mathrm{R} \\ 0 \mathrm{for} \mathrm{r}>\mathrm{R} \right\} \end{gathered}$$

where ${\mathrm{\rho }}_{\mathrm{o}}$ is a constant. A test mass can undergo circular motion under the influence of the gravitational field of particles. Its speed $\mathrm{v}$ as a function of distance $\mathrm{r}\left(0<\mathrm{r}<\infty \right)$ from the centre of the system is represented by :

A black hole is an object whose gravitational field is so strong that even light cannot escape from it. To what approximate radius earth $\left(\mathrm{mass}=5.98\times {10}^{24}\mathrm{kg}\right)$ have to be a compressed black hole?

Dependent of intensity of gravitational field $\left(\mathrm{E}\right)$ of earth with distance $\left(\mathrm{r}\right)$ from centre of earth is correctly represented $\mathrm{y}$: