Two satellites, $A$ and $B,$ have masses $m$ and $2\,m$ respectively. $A$ is in a circular orbit of radius $R,$ and $B$ is in a circular orbit of radius $2R$ around the earth. The ratio of their kinetic energies, $K.E._A / K.E._B ,$ is

In an orbit if the time of revolution of a satellite is $T$, then $P E$ is proportional to

A satellite of mass $\mathrm{m}$ is launched vertically upwards with an initial speed $u$ from the surface of the earth. After it reaches height $\mathrm{R}$ ($R =$ radius of the earth), it ejects a rocket of mass $\frac{\mathrm{m}}{10}$ so that subsequently the satellite moves in a circular orbit. The kinetic energy of the rocket is

($G$ is the gravitational constant: $\mathrm{M}$ is the mass of the earth)

Two planets have masses $M$ and $16\, M$ and their radii are $a$ and $2\, a$ respectively. The separation between the centres of the planets is $10\, a.$ A body of mass $m$ is fired from the surface of the larger planet towards the smaller planet along the line joining their centres. For the body to be able to reach at the surface of smaller planet, the minimum firing speed needed is

In case of an orbiting satellite, if the radius of orbit is decreased