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QJEEM12Ph7da6: JEE Main 2012 Physics - Class 11 JEEM12Ph7da6 Solution: The mass of a spaceship is It is to be launched from the…

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:

Step-by-Step Verified Solution

Potential energy at earth surface =

- {{GMm} \over R}

and at free space potential energy = 0

Work done for this =

0 - \left( { - {{GMm} \over R}} \right)

{{{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 \times 10 \times 6400 \times {10^3}

= 6.4 \times {10^{10}}\,\,

Joules