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 $\,J$)?

What is the potential energy of a satellite at a height of $6.4 \times 10^6 \, m$ from the surface of the Earth? ($R_e$ = radius of the Earth)

The masses $m$ in figures $(A)$ and $(B)$ are identical. The gravitational potential energy in the two cases are $U_A$ and $U_B$. Then

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 $\text{ J}$)

Gravitational potential difference between the surface of a planet and a point situated at a height of $20\,m$ above its surface is $2\,J/kg$. If the gravitational field is uniform,then the work done in taking a $5\,kg$ body to a height of $4\,m$ above the surface will be ........ $J$.

Two concentric shells have masses $M$ and $m$ and their radii are $R$ and $r$ respectively,where $R > r$. If $x$ is the distance from the common centre,what is the gravitational potential at a point for which $r < x < R$?