Question

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 the earth) is 10 m/s² and 6400 km respectively. The required energy for this work will be

(a) 6.4 x 10¹⁰ Joules

(b) 6.4 x 10¹¹ Joules

(c) 6.4 x 10⁸ Joules

(d) 6.4 x 10⁹ Joules

Answer 1

The correct answer is option (a) 6.4 x 10¹⁰ Joules 

Explaination ::

The energy required is given by = \(GMm\over R\)

=\( gR^2 \times{ m\over R} (∵ g = {GM\over R2}) \)= mgR

= 1000 x 10 x 6400 x 10³

= 64 x 10⁹ J

= 6.4 x 10¹⁰ J