Exams › JEE Advanced › Physics
A satellite of mass m is placed into a circular orbit at radius 2R from Earth's center, starting from rest on Earth's surface. Subsequently, it is transferred from that orbit to a higher circular orbit at radius 3R from Earth's center. Express (i) the energy needed to put the satellite into the 2R orbit from Earth's surface, and (ii) the additional energy required to move it from the 2R orbit to the 3R orbit, in terms of m, g, and R (where R is Earth's radius and g is gravitational acceleration at the surface).
- 3mgR/4 and mgR/12
- mgR/4 and mgR/12
- 3mgR/4 and mgR/6
- None of these
Correct answer: 3mgR/4 and mgR/12
Solution
The total energy at orbit 2R is -GMm/4R and at Earth's surface is -GMm/R, giving a difference of 3GMm/4R = 3mgR/4. Moving from 2R to 3R changes energy from -GMm/4R to -GMm/6R, a difference of GMm/12R = mgR/12.
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