A $400 \;kg$ satellite is in a circular orbit of radius $2 R_{E}$ about the Earth. How much energy is required to transfer it to a circular orbit of radius $4 R_{E} ?$ What are the changes in the kinetic and potential energles?

A particle of mass $m$ moves around the origin in a potential $\frac{1}{2} m \omega^{2} r^{2}$, where $r$ is the distance from the origin. Applying the Bohr's model in this case, the radius of the particle in its $n$th orbit in terms of $a=\sqrt{h /(2 \pi m \omega)}$ is

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

The work done to raise a mass $\mathrm{m}$ from the surface of the earth to a height $\mathrm{h}$, which is equal to the radius of the earth, is 

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