What is the minimum energy required to launch a satellite of mass m from the surface of a planet of mass M and radius R in a circular orbit at an altitude of 2R?

5GmM/6R

2GmM/3R

GmM/2R

GmM/3R

Solution

5GmM/6R

From conservation of energy,
Total energy at the planet = Total energy at the altitude
$negative GMm over straight R space plus space left parenthesis KE right parenthesis subscript surface space equals space minus fraction numerator GMm over denominator 3 straight R end fraction space plus space 1 half mv subscript straight A superscript 2 space... space left parenthesis straight i right parenthesis$
In its orbit the necessary centripetal force provided by gravitational force.
∴ $therefore space fraction numerator mv subscript straight A superscript 2 over denominator left parenthesis straight R space plus 2 straight R right parenthesis end fraction space equals space fraction numerator GMm over denominator left parenthesis straight R space plus 2 straight R right parenthesis squared end fraction straight v subscript straight A superscript 2 space equals space fraction numerator GM over denominator 3 straight R end fraction space... space left parenthesis ii right parenthesis From space eq space left parenthesis straight i right parenthesis space and space left parenthesis ii right parenthesis space we space get left parenthesis KE right parenthesis subscript surface space equals space 5 over 6 GMm over straight R$

Some More Questions From Motion in Straight Line Chapter

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Motion In Straight Line

What is the minimum energy required to launch a satellite of mass m from the surface of a planet of mass M and radius R in a circular orbit at an altitude of 2R?

5GmM/6R

2GmM/3R

GmM/2R

GmM/3R

Some More Questions From Motion in Straight Line Chapter

What is rest?

What is motion?

Is absolute rest or absolute motion possible?

What is the most essential thing to study the motion of a body?

Can a body be always at rest in some frame?

Can a body be in motion in the frame associated with the body itself?

When an object in motion can be considered as particle or point object?

Can you think of physical phenomena involving the moon in which moon cannot be treated as particle?

A train is crossing the bridge. Can it be taken as a particle?

Can a train be taken a particle? Give an example in support of your answer.

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Motion In Straight Line

What is the minimum energy required to launch a satellite of mass m from the surface of a planet of mass M and radius R in a circular orbit at an altitude of 2R? 5GmM/6R 2GmM/3R GmM/2R GmM/3R

Some More Questions From Motion in Straight Line Chapter

What is rest?

What is motion?

Is absolute rest or absolute motion possible?

What is the most essential thing to study the motion of a body?

Can a body be always at rest in some frame?

Can a body be in motion in the frame associated with the body itself?

When an object in motion can be considered as particle or point object?

Can you think of physical phenomena involving the moon in which moon cannot be treated as particle?

A train is crossing the bridge. Can it be taken as a particle?

Can a train be taken a particle? Give an example in support of your answer.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

What is the minimum energy required to launch a satellite of mass m from the surface of a planet of mass M and radius R in a circular orbit at an altitude of 2R?

5GmM/6R

2GmM/3R

GmM/2R

GmM/3R