Two satellites $A$ and $B$ , having ratio of masses $3 : 1$ are in circular orbits of radius $r$ and $4r$ . Calculate the ratio of total mechanical energy of $A$ and $B$

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

Two stars of masses $3\times10^{31}\, kg$ each, and at distance $2\times10^{11}\, m$ rotate in a plane about their common centre of mass $O. A$ meteorite passes through $O$ moving perpendicular to the star’s rotation plane. In order to escape from the gravitational field of this double star, the minimum speed that meteorite should have at $O$ is : (Take Gravitational constant $G = 6.67\times10^{-11}\, Nm^2\, kg^{-2}$)

What is the change in the potential energy going away from earth and coming near to the earth ?

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