The mass of a spaceship is 1000kg. It is to be launched from the earth's surface out into free space. The value of g and R (radius of earth) are `10m/s^2` and 6400 km respectively. The required energy for this work will be:

Options

A. `6.4xx10^(8)` joule
B. `6.4xx10^(9)` joule
C. `6.4xx10^(10)` joule
D. `6.4xx10^(11)` joule

Answer

C

Explanation

At the surface of the earth, `P.E.=-(GMm)/(R )`
`therefore` Energy required to launch it in free space
`=(GMm)/(R )" " [because g = (GM)/(R^(2))]`
`therefore E = (gR^(2)m)/(R )`
`= mgR`
`= 1000xx10xx6400xx10^(3)`
`=64xx10^(9)J=6.4xx10^(10)J`