The mass of a spaceship is 1000 kg. It is to be launched

The mass of a spaceship is 1000 kg. It is to be launched from the earth's surface out into free space. The value of 'g' and 'R' (radius of earth) are 10 m/s2 and 6400 km respectively. The required energy for this work will be

  1. 6.4 X 108 Joules
  2. 6.4 X 109 Joules
  3. 6.4 X 1010 Joules
  4. 6.4 X 1011 Joules

Answer

To launch the spaceship out into free space, from energy conservation,

- (GMm/R) + E = 0

E = GMm/R = (GMmR)/R2 = mgR

= 6.4 x 1010 J

The correct option is C.