The additional kinetic energy to be provided to a satellite of mass $m$ revolving around a planet of mass $M$, to transfer it from a circular orbit of radius $R_1$ to another of radius $R_2\,(R_2 > R_1)$ is
$GmM\,\left( {\frac{1}{{{R_1}}} - \frac{1}{{{R_2}}}} \right)$
$2GmM\,\left( {\frac{1}{{{R_1}}} - \frac{1}{{{R_2}}}} \right)$
$\frac{1}{2}GmM\,\left( {\frac{1}{{{R_1}}} - \frac{1}{{{R_2}}}} \right)$
$GmM\,\left( {\frac{1}{{R_1^2}} - \frac{1}{{R_2^2}}} \right)$
Gravitation is the phenomenon of interaction between ............
A body of mass $m$ is situated at a distance equal to $2R$ ($R-$ radius of earth) from earth's surface. The minimum energy required to be given to the body so that it may escape out of earth's gravitational field will be
A satellite is launched into a circular orbit of radius $R$ around earth, while a second satellite is launched into a circular orbit of radius $1.02\, {R}$. The percentage difference in the time periods of the two satellites is -
Suppose the gravitational force varies inversely as the $n^{th}$ power of distance. Then the time period of a planet in circular orbit of radius $R$ around the sun will be proportional to
Two spheres of masses $m$ and $M$ are situated in air and the gravitational force between them is $F.$ The space around the masses is now filled with a liquid of specific gravity $3.$ The gravitational force will now be