The gravitational field in a region is given by $\vec{g} = 5\,N/kg\hat{i} + 12\,N/kg\hat{j}$. The change in the gravitational potential energy of a particle of mass $1\,kg$ when it is taken from the origin to a point $(7\,m, -3\,m)$ is ....... $J$.

In a certain region of space,the gravitational field is given by $E = -k/r$,where $r$ is the distance and $k$ is a constant. If the gravitational potential at $r = r_0$ is $V_0$,then what is the expression for the gravitational potential $V$?

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

Why does the potential energy of an object increase when it is raised above the surface of the Earth?

The gravitational potential energy of a body on the surface of the earth is $E$. If the body is taken from the surface of the earth to a height equal to $150 \%$ of the radius of the earth,its gravitational potential energy is (in $E$)

$A$ particle of mass $10\, g$ is kept on the surface of a uniform sphere of mass $100\, kg$ and radius $10\, cm$. Find the work to be done against the gravitational force between them to take the particle far away from the sphere (you may take $G = 6.67 \times 10^{-11}\, Nm^2 / kg^2$).