A particle of mass \(m\) is thrown upwards from the surface of the earth, with a velocity \(u.\) The mass and the radius of the earth are, respectively, \(M\) and \(R.\) \(G\) is the gravitational constant and \(g\) is the acceleration due to gravity on the surface of the earth. The minimum value of \(u\) so that the particle does not return back to earth is:

1. \(\sqrt{\dfrac{2 {GM}}{{R}^2}} \)

2. \(\sqrt{\dfrac{2 {GM}}{{R}}} \)

3.\(\sqrt{\dfrac{2 {gM}}{{R}^2}} \)

4. \(\sqrt{ {2gR^2}}\)

If the radius of a planet is \(R\) and its density is \(\rho, \) the escape velocity from its surface will be

1. \(V_{e} \propto p R\)                         

2. \(V_{e} \propto R \sqrt{\rho}\)

 3. \(V_{e} \propto \dfrac{\sqrt{p}}{R}\)                        

4. \(V_{e} \propto \dfrac{1}{\sqrt{p} R}\)