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:

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

The gravitational field in a region is given by the equation $E = (5\hat{i} + 12\hat{j}) \,N/kg$. If a particle of mass $2 \,kg$ is moved from the origin to the point $(12 \,m, 5 \,m)$ in this region, what is the change in gravitational potential energy (in $\,J$)?

Consider two configurations of a system of three particles of masses $m, 2m$ and $3m$. The work done by an external agent in changing the configuration of the system from figure $(i)$ to figure $(ii)$ is:

Two particles of mass $m$ and $9m$ are separated by a distance $r$. At a point on the line joining them,the gravitational field is zero. What is the gravitational potential at that point? ($G$ is the universal gravitational constant)

If three particles each of mass $M$ are placed at the corners of an equilateral triangle of side $a$,the potential energy of the system and the work done if the side of the triangle is changed from $a$ to $2a$,are