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An artificial satellite moving in a circular orbit around the earth has a total (kinetic + potential) energy E0. Its potential energy is
- a)-E0
- b)1.5 E0
- c)2E0
- d)E0
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
An artificial satellite moving in a circular orbit around the earth ha...
Explanation:
When an artificial satellite moves in a circular orbit around the earth, it experiences a gravitational force towards the center of the earth, which provides the necessary centripetal force to keep the satellite in the circular orbit.
The total energy of the satellite is the sum of its kinetic energy and potential energy.
1. Kinetic Energy of the Satellite:
The kinetic energy of the satellite is given by the formula:
KE = (1/2)mv^2
where m is the mass of the satellite and v is its velocity.
In a circular orbit, the velocity of the satellite is given by:
v = √(GM/r)
where G is the gravitational constant, M is the mass of the earth, and r is the radius of the orbit.
Substituting the value of v in the formula for KE, we get:
KE = (1/2)m(GM/r)
KE = (1/2)(GMm/r)
2. Potential Energy of the Satellite:
The potential energy of the satellite is given by the formula:
PE = -GMm/r
where G is the gravitational constant, M is the mass of the earth, m is the mass of the satellite, and r is the radius of the orbit.
3. Total Energy of the Satellite:
The total energy of the satellite is the sum of its kinetic energy and potential energy:
E0 = KE + PE
E0 = (1/2)(GMm/r) - (GMm/r)
E0 = -(1/2)(GMm/r)
Therefore, the potential energy of the satellite is given by:
PE = -E0/2
PE = -1/2(KE)
PE = -1/2(E0 - PE)
PE = -1/2E0 + 1/2PE
2PE = -E0
PE = -E0/2
Hence, option C is the correct answer: 2E0.
When an artificial satellite moves in a circular orbit around the earth, it experiences a gravitational force towards the center of the earth, which provides the necessary centripetal force to keep the satellite in the circular orbit.
The total energy of the satellite is the sum of its kinetic energy and potential energy.
1. Kinetic Energy of the Satellite:
The kinetic energy of the satellite is given by the formula:
KE = (1/2)mv^2
where m is the mass of the satellite and v is its velocity.
In a circular orbit, the velocity of the satellite is given by:
v = √(GM/r)
where G is the gravitational constant, M is the mass of the earth, and r is the radius of the orbit.
Substituting the value of v in the formula for KE, we get:
KE = (1/2)m(GM/r)
KE = (1/2)(GMm/r)
2. Potential Energy of the Satellite:
The potential energy of the satellite is given by the formula:
PE = -GMm/r
where G is the gravitational constant, M is the mass of the earth, m is the mass of the satellite, and r is the radius of the orbit.
3. Total Energy of the Satellite:
The total energy of the satellite is the sum of its kinetic energy and potential energy:
E0 = KE + PE
E0 = (1/2)(GMm/r) - (GMm/r)
E0 = -(1/2)(GMm/r)
Therefore, the potential energy of the satellite is given by:
PE = -E0/2
PE = -1/2(KE)
PE = -1/2(E0 - PE)
PE = -1/2E0 + 1/2PE
2PE = -E0
PE = -E0/2
Hence, option C is the correct answer: 2E0.
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Community Answer
An artificial satellite moving in a circular orbit around the earth ha...
Kinetic energy KE = GMm/2r
Total energy = -GMm/2r = E•
potential energy = total energy - Kinetic energy
PE = -GMm/2r - GMm/2r
»» -GMm/2r
PE = 2E•
Total energy = -GMm/2r = E•
potential energy = total energy - Kinetic energy
PE = -GMm/2r - GMm/2r
»» -GMm/2r
PE = 2E•
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An artificial satellite moving in a circular orbit around the earth has a total (kinetic + potential) energy E0. Its potential energy isa)-E0b)1.5 E0c)2E0d)E0Correct answer is option 'C'. Can you explain this answer?
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