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The total energy of an artificial satellite of mass m revolving in a circular orbit around the Earth with a speed v is (a) 1/2 mv^2 (b) -1/4 mv^2 (c) -1/2 mv^2 (d) 1/2 mv^2 The answer is (c). Explain?
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The total energy of an artificial satellite of mass m revolving in a c...
Total Energy of an Artificial Satellite
The total energy of a satellite in orbit consists of its kinetic and potential energy. Let's break down these components:
Kinetic Energy (KE)
- The kinetic energy of the satellite is given by the formula:
KE = 1/2 mv^2
- Here, m is the mass of the satellite and v is its orbital speed.
Gravitational Potential Energy (PE)
- The gravitational potential energy of the satellite in orbit is given by:
PE = -GMm/r
- G is the gravitational constant, M is the mass of the Earth, and r is the distance from the center of the Earth to the satellite.
Relationship Between KE and PE
- For a satellite in a stable circular orbit, the gravitational force provides the necessary centripetal force. Thus, we can relate the kinetic energy to the potential energy:
- KE = -1/2 PE
- This relationship leads to the conclusion that the potential energy is negative because it is defined as zero at an infinite distance from the Earth.
Total Energy (E)
- The total energy of the satellite is the sum of its kinetic and potential energy:
E = KE + PE
- Substituting the expressions, we find:
E = 1/2 mv^2 - GMm/r
- With the relation between KE and PE, we can express the total energy as:
E = -1/2 mv^2
Conclusion
- Therefore, the total energy of an artificial satellite in circular orbit is:
E = -1/2 mv^2
- This negative value indicates that the satellite is in a bound gravitational state, confirming that the correct answer is (c) -1/2 mv^2.
The total energy of a satellite in orbit consists of its kinetic and potential energy. Let's break down these components:
Kinetic Energy (KE)
- The kinetic energy of the satellite is given by the formula:
KE = 1/2 mv^2
- Here, m is the mass of the satellite and v is its orbital speed.
Gravitational Potential Energy (PE)
- The gravitational potential energy of the satellite in orbit is given by:
PE = -GMm/r
- G is the gravitational constant, M is the mass of the Earth, and r is the distance from the center of the Earth to the satellite.
Relationship Between KE and PE
- For a satellite in a stable circular orbit, the gravitational force provides the necessary centripetal force. Thus, we can relate the kinetic energy to the potential energy:
- KE = -1/2 PE
- This relationship leads to the conclusion that the potential energy is negative because it is defined as zero at an infinite distance from the Earth.
Total Energy (E)
- The total energy of the satellite is the sum of its kinetic and potential energy:
E = KE + PE
- Substituting the expressions, we find:
E = 1/2 mv^2 - GMm/r
- With the relation between KE and PE, we can express the total energy as:
E = -1/2 mv^2
Conclusion
- Therefore, the total energy of an artificial satellite in circular orbit is:
E = -1/2 mv^2
- This negative value indicates that the satellite is in a bound gravitational state, confirming that the correct answer is (c) -1/2 mv^2.
Community Answer
The total energy of an artificial satellite of mass m revolving in a c...
T E= -KE
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The total energy of an artificial satellite of mass m revolving in a circular orbit around the Earth with a speed v is (a) 1/2 mv^2 (b) -1/4 mv^2 (c) -1/2 mv^2 (d) 1/2 mv^2 The answer is (c). Explain?
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The total energy of an artificial satellite of mass m revolving in a circular orbit around the Earth with a speed v is (a) 1/2 mv^2 (b) -1/4 mv^2 (c) -1/2 mv^2 (d) 1/2 mv^2 The answer is (c). Explain? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about The total energy of an artificial satellite of mass m revolving in a circular orbit around the Earth with a speed v is (a) 1/2 mv^2 (b) -1/4 mv^2 (c) -1/2 mv^2 (d) 1/2 mv^2 The answer is (c). Explain? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The total energy of an artificial satellite of mass m revolving in a circular orbit around the Earth with a speed v is (a) 1/2 mv^2 (b) -1/4 mv^2 (c) -1/2 mv^2 (d) 1/2 mv^2 The answer is (c). Explain?.
The total energy of an artificial satellite of mass m revolving in a circular orbit around the Earth with a speed v is (a) 1/2 mv^2 (b) -1/4 mv^2 (c) -1/2 mv^2 (d) 1/2 mv^2 The answer is (c). Explain? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about The total energy of an artificial satellite of mass m revolving in a circular orbit around the Earth with a speed v is (a) 1/2 mv^2 (b) -1/4 mv^2 (c) -1/2 mv^2 (d) 1/2 mv^2 The answer is (c). Explain? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The total energy of an artificial satellite of mass m revolving in a circular orbit around the Earth with a speed v is (a) 1/2 mv^2 (b) -1/4 mv^2 (c) -1/2 mv^2 (d) 1/2 mv^2 The answer is (c). Explain?.
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