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AIEEE 2012 Solved Paper

Section: Physics

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Question : 36 of 89

Marks: +1, -0

The mass of a spaceship is

1000 \text{ kg}

. It is to be launched from the earth's surface out into free space. The value of

g

R

(radius of earth) are

10 \text{ m} / \text{s}^2

6400 \text{ km}

respectively. The required energy for this work will be:

$6.4 \times 10^{11}$ Joules
$6.4 \times 10^8$ Joules
$6.4 \times 10^9$ Joules
$6.4 \times 10^{10}$ Joules

Solution:

Potential energy at earth surface

= -\frac{G M m}{R}

and at free space potential energy

=0

Work done for this

=0- \left(-\frac{G M m}{R}\right) = \frac{G M m}{R}

So the required energy for this work is

\;=\;\frac{G M m}{R}

\;=\;\frac{g R^2 m}{R} \left[\;\text{as}\; g=\frac{G M}{R^2}\right]

\;=m g R

\;=1000 \times 10 \times 6400 \times 10^3

\;=6.4 \times 10^{10} \;\text{ Joules }\;

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