If the mass of the Earth is $M$,its radius is $R$,and the gravitational constant is $G$,then the work done to take a $1 \, kg$ mass from the Earth's surface to infinity will be:

$A$ geostationary satellite orbits the Earth at a height of nearly $36,000 \; km$ from the surface of the Earth. What is the potential due to Earth's gravity at the site of this satellite? (Take the potential energy at infinity to be zero). Mass of the Earth $= 6.0 \times 10^{24} \; kg$,radius $= 6400 \; km$.

If the gravitational potential energy of two point masses infinitely away is taken to be zero,then the gravitational potential energy of a galaxy is ...............

Potential energy of a satellite having mass $m$ and rotating at a height of $6.4 \times 10^6 \ m$ from the Earth's surface is

If one wants to remove all the mass of the earth to infinity in order to break it up completely,the amount of energy that needs to be supplied will be $\frac{x}{5} \frac{GM^2}{R}$,where $x$ is .......... (Round off to the Nearest Integer). ($M$ is the mass of earth,$R$ is the radius of earth,$G$ is the gravitational constant)

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 ....... $J$.