$A$ body of mass $m$ rises to a height $h = R/5$ from the earth's surface,where $R$ is the earth's radius. If $g$ is the acceleration due to gravity at the earth's surface,the increase in potential energy is:

Four particles each of mass $m$ are placed at four vertices of a rectangle having side lengths $3 l_o$ and $4 l_o$. The magnitude of the gravitational potential energy of the system in units of $\frac{Gm^2}{l_o}$ is:

The gravitational field in a region is given by the equation $E = (5\hat{i} + 12\hat{j}) \text{ N/kg}$. If a particle of mass $2 \text{ kg}$ is moved from the origin $(0, 0)$ to the point $(12 \text{ m}, 5 \text{ m})$ in this region, the change in gravitational potential energy is: (in $\text{ J}$)

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 ....... $J$.

Write an equation for the potential energy of a satellite. Why is the potential energy of a satellite negative?

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?