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  4. 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 :

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Q. 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 $10\, m/s^2$ and $6400\, km$ respectively. The required energy for this work will be :

AIEEEAIEEE 2012Gravitation

Solution:

$W=0-\left(-\frac{GMm}{R}\right)=\frac{GMm}{R}$
$=gR^{2}\times \frac{m}{R}=mgR$
$= 1000 × 10 × 6400 × 10^{3}$
$= 64 × 10^{9}\, J$
$= 64 × 10^{10}$