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
$GmM\,\left( {\frac{1}{{{R_1}}} - \frac{1}{{{R_2}}}} \right)$
$2GmM\,\left( {\frac{1}{{{R_1}}} - \frac{1}{{{R_2}}}} \right)$
$\frac{1}{2}GmM\,\left( {\frac{1}{{{R_1}}} - \frac{1}{{{R_2}}}} \right)$
$GmM\,\left( {\frac{1}{{R_1^2}} - \frac{1}{{R_2^2}}} \right)$
The magnitudes of gravitational field at distances $r_1$ and $r_2$ from the centre of a uniform sphere of radius $R$ and mass $M$ are $F_1$ and $F_2$ respectively. Then-
A body of mass $m$ is situated at distance $4R_e$ above the Earth's surface, where $R_e$ is the radius of Earth how much minimum energy be given to the body so that it may escape
When a body is taken from pole to the equator its weight
A satellite $S$ is moving in an elliptical orbit around the earth. The mass of the satellite is very small compared to the mass of the earth. Then
A particle of mass $M$ is placed at the centre of a uniform spherical shell of mass $2M$ and radius $R$. The gravitational potential on the surface of the shell is