With what velocity should a particle be projected so that its height becomes equal to the radius of the earth?

1.  ${\left(\frac{GM}{R}\right)}^{1/2}$

2. ${\left(\frac{8GM}{R}\right)}^{1/2}$

3.  ${\left(\frac{2GM}{R}\right)}^{1/2}$

4.  ${\left(\frac{4GM}{R}\right)}^{1/2}$

If a body of mass \(m\) placed on the earth's surface is taken to a height of \(h = 3R,\) then the change in gravitational potential energy is:

1. \(\dfrac{mgR}{4}\)

2. \(\dfrac{2}{3} mgR\)

3. \(\dfrac{3}{4} mgR\)

4. \(\dfrac{mgR}{2}\)