A particle is projected from the surface of the earth with a velocity equal to twice the escape velocity. When particle is very far from the earth. Its speed would be

The time period of revolution of a satellite $T$ around the carth depends on the radius of the circular orbit $R$. mass of the earth $M$ and universal gravitational constant $G$. The expression for $T$, using dimensional analysis is ( $K$ is constant of proportionality)

If the time period of revolution of a satellite is $T$, the its kinetic energy is proportional to

What is the height from the surface of earth, where acceleration due to gravity will be $1 / 4$ of that of the earth? $\left(R_E=6400 \mathrm{~km}\right)$