The time period of a satellite of earth is 24 hours. If the separation between the earth and the satellite is decreased to one fourth of the previous value then its new time period will become

A body is projected vertically from earth's surface with $\left(\frac{1}{3}\right)^{\mathrm{rd}}$ of escape velocity. The maximum height reached by the body is ( $R=$ radius of earth)

The escape velocity of a satellite from the surface of earth does NOT depend on