Question 228: 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: