A body of mass \(m\) is taken from the Earth’s surface to the height equal to twice the radius \((R)\) of the Earth. The change in potential energy of the body will be: 

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. \(\dfrac{mgR}{2}\)

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