At what height above the earth's surface is the value of $'g'$ is same as in a $200\, km$ deep mine ........ $km$

A planet is revolving ground the sun in an elliptical orbit. Its closest distance from the sun is $r_{min}$, the farthest distance from the sun is $r_{max}$. If the orbital angular velocity of the planet when it is the nearest to the sun is $\omega $, then the orbital angular velocity at the point when it is at the farthest distance from the sun is 

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 :-

Which graph correctly presents the variation of acceleration due to gravity with the distance from the centre of the earth (radius of the earth $= R_E$ )?

A geostationary satellite is revolving around the earth. To make it escape from gravitational field of earth, is velocity must be increased ........ $\%$

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