The kinetic energy needed to project a body of mass m from the earth's surface to infinity is

1. \(\frac14\) mgR

2. \(\frac12\) mgR

3. mgR

4. 2 mgR

A particle is kept at rest at a distance R (earth's radius) above the earth's surface. The minimum speed with which it should be projected so that it does not return is

1. \(\sqrt\frac{GM}{4R}\)

2. \(\sqrt\frac{GM}{2R}\)

3. \(\sqrt\frac{GM}{R}\)

4. \(\sqrt\frac{2GM}{R}\)

A satellite is orbiting the earth close to its surface. A particle is to be projected from the satellite to just escape from the Earth. The escape speed from the Earth is \(v_e.\) Its speed with respect to the satellite: