Question 212: Gravitation

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 earth ) are $10\,m/{s^2}$ and $6400$ $km$ respectively. The required energy for this work will be:

Accepted Answer

Potential energy at earth surface = $ - {{GMm} \over R}$
and at free space potential energy = 0
Work done for this = $0 - \left( { - {{GMm} \over R}} ight)$ = ${{{GMm} \over R}}$
So the required energy for this work is
= ${{GMm} \over R}$
=${{{g{R^2}m} \over R}}$ [ as $g = {{GM} \over {{R^2}}}$ ]
= $mgR$
$ = 1000 	imes 10 	imes 6400 	imes {10^3}$
$ = 6.4 	imes {10^{10}}\,\,$ Joules

Answer

$6.4 	imes {10^{11}}\,$ Joules

Answer

$6.4 	imes {10^8}\,$ Joules

Answer

$6.4 	imes {10^9}\,$ Joules

Answer

$6.4 	imes {10^{10}}\,$ Joules

Gravitation

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:

Choose the correct answer: