Radius of the earth is $R$. If a body is taken to a height $3R$ from the surface of the earth than change in potential energy will be
$3mgR$
$\frac {3}{2}\,mgR$
$mgR$
$\frac {3}{4}\,mgR$
The rotation of the earth having $R$ radius about its axis speeds up to a value such that a man at latitude angle $60^o$ feels weightlessness. The duration of the day in such a case is.
The variation of acceleration due to gravity $ ( g )$ with distance $(r)$ from the center of the earth is correctly represented by ... (Given $R =$ radius of earth)
A geostationary satellite is orbiting the earth at a height of $6\,R$ above the surface of earth ($R$ is the radius of earth). The time period of another satellite at a height of $2.5\,R$ from the surface of the earth is :-
In order to shift a body of mass $m$ from a circular orbit of radius $3R$ to a higher radius $5R$ around the earth, the work done is
A particle of mass $M$ is at a distance $'a'$ from surface of a thin spherical shell of uniform equal mass and having radius $a$