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Question

An artificial satellite revolves around the earth in a circular orbit with a speed $$v$$. If $$m$$ is the mass of the satellite, its total energy is :


A
12mv2
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B
12mv2
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C
mv2
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D
32mv2
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Solution

The correct option is D $$-\dfrac { 1 }{ 2 } m{ v }^{ 2 }$$
Kinetic energy of satellite, $$KE = \dfrac { 1 }{ 2 } m{ v }^{ 2 }$$
where $$v = \sqrt { \dfrac { GM }{ r }  } $$
Potential energy of satellite,
$$PE = \dfrac { -GMm }{ r } = -m{ v }^{ 2 }$$
$$\therefore$$ Total energy $$ = KE + PE$$
                      $$=\dfrac { 1 }{ 2 } m{ v }^{ 2 } - m{ v }^{ 2 } = -\dfrac { 1 }{ 2 } m{ v }^{ 2 }$$

Physics

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