If an artificial satellite is moving in a circular orbit around the earth with a speed equal to half the magnitude of the escape velocity from the earth, the height of the satellite above the surface of the earth is

A body of mass $m$ falls from a height $R$ above the surface of the earth, where $R$ is the radius of the earth. What is the velocity attained by the body on reaching the ground? (Acceleration due to gravity on the surface of the earth is $g$)

If the acceleration due to gravity at earth is $'g'$ and mass of earth is $80$ times that of moon and radius of earth is $4$ times that of moon, the value of acceleration due to gravity at the surface of moon will be

Suppose the gravitational force varies inversely as the $n^{th}$ power of the distance. Then, the time period of a planet in circular orbit of radius $R$ around the sun will be proportional to

The change in the value of $‘g’$ at a height $‘h’$ above the surface of the earth is the same as at a depth $‘d’$ below the surface of earth. When both $‘d’$ and $‘h’$ are much smaller than the radius of earth, then which one of the following is correct?

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 :-