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Two satellites of earth, S1 and S2, are moving in the same orbit. The mass of S1 is four times the mass of S2. Which one of the following statements is true?
- a)The time period of S1 is four times that of S2.
- b)The potential energies of earth and satellite in the two cases are equal.
- c)S1 and S2 are moving with the same speed.
- d)The kinetic energies of the two satellites are equal.
Correct answer is option 'C'. Can you explain this answer?
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Two satellites of earth, S1 and S2, are moving in the same orbit. The ...
Explanation:
The given problem states that S1 and S2 are moving in the same orbit. This means that they are at the same distance from the center of the earth and are experiencing the same gravitational force. However, the mass of S1 is four times that of S2. Let us analyze the given options one by one to determine which one(s) is/are true.
a) The time period of S1 is four times that of S2.
The time period of a satellite is directly proportional to the square root of the cube of the semi-major axis of its orbit and inversely proportional to the square root of the mass of the central body. Since S1 and S2 are in the same orbit, their semi-major axes are equal. However, S1 has four times the mass of S2. Therefore, the time period of S1 will be more than that of S2, but not four times more. Hence, this option is false.
b) The potential energies of earth and satellite in the two cases are equal.
The potential energy of a satellite is given by -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 distance between the center of the earth and the satellite. Since S1 and S2 are at the same distance from the earth, their potential energies will be equal only if their masses are equal. However, S1 has four times the mass of S2. Therefore, the potential energy of S1 will be four times more than that of S2. Hence, this option is false.
c) S1 and S2 are moving with the same speed.
Since S1 and S2 are in the same orbit, they are experiencing the same gravitational force. According to Newton's second law of motion, F = ma, where F is the gravitational force, m is the mass of the satellite, and a is the acceleration due to gravity. Since the force is the same for both satellites and S1 has four times the mass of S2, S1 will experience one-fourth the acceleration of S2. As a result, both satellites will move at the same speed. Hence, this option is true.
d) The kinetic energies of the two satellites are equal.
The kinetic energy of a satellite is given by (1/2)mv^2, where m is the mass of the satellite and v is its velocity. Since S1 and S2 are moving at the same speed, their kinetic energies will be equal only if their masses are equal. However, S1 has four times the mass of S2. Therefore, the kinetic energy of S1 will be four times more than that of S2. Hence, this option is false.
Conclusion:
The correct option is (c) S1 and S2 are moving with the same speed.
The given problem states that S1 and S2 are moving in the same orbit. This means that they are at the same distance from the center of the earth and are experiencing the same gravitational force. However, the mass of S1 is four times that of S2. Let us analyze the given options one by one to determine which one(s) is/are true.
a) The time period of S1 is four times that of S2.
The time period of a satellite is directly proportional to the square root of the cube of the semi-major axis of its orbit and inversely proportional to the square root of the mass of the central body. Since S1 and S2 are in the same orbit, their semi-major axes are equal. However, S1 has four times the mass of S2. Therefore, the time period of S1 will be more than that of S2, but not four times more. Hence, this option is false.
b) The potential energies of earth and satellite in the two cases are equal.
The potential energy of a satellite is given by -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 distance between the center of the earth and the satellite. Since S1 and S2 are at the same distance from the earth, their potential energies will be equal only if their masses are equal. However, S1 has four times the mass of S2. Therefore, the potential energy of S1 will be four times more than that of S2. Hence, this option is false.
c) S1 and S2 are moving with the same speed.
Since S1 and S2 are in the same orbit, they are experiencing the same gravitational force. According to Newton's second law of motion, F = ma, where F is the gravitational force, m is the mass of the satellite, and a is the acceleration due to gravity. Since the force is the same for both satellites and S1 has four times the mass of S2, S1 will experience one-fourth the acceleration of S2. As a result, both satellites will move at the same speed. Hence, this option is true.
d) The kinetic energies of the two satellites are equal.
The kinetic energy of a satellite is given by (1/2)mv^2, where m is the mass of the satellite and v is its velocity. Since S1 and S2 are moving at the same speed, their kinetic energies will be equal only if their masses are equal. However, S1 has four times the mass of S2. Therefore, the kinetic energy of S1 will be four times more than that of S2. Hence, this option is false.
Conclusion:
The correct option is (c) S1 and S2 are moving with the same speed.
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Community Answer
Two satellites of earth, S1 and S2, are moving in the same orbit. The ...
The satellites are orbitting earth that means they moving with critical velo. The formula for crit. velo. is rootGM/r^2so critical velo. is independent of mass of satellite therefore both have same velo.M=mass of earth.
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Two satellites of earth, S1 and S2, are moving in the same orbit. The mass of S1 is four times the mass of S2. Which one of the following statements is true?a) The time period of S1 is four times that of S2. b) The potential energies of earth and satellite in the two cases are equal. c) S1 and S2 are moving with the same speed. d) The kinetic energies of the two satellites are equal. Correct answer is option 'C'. Can you explain this answer?
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Two satellites of earth, S1 and S2, are moving in the same orbit. The mass of S1 is four times the mass of S2. Which one of the following statements is true?a) The time period of S1 is four times that of S2. b) The potential energies of earth and satellite in the two cases are equal. c) S1 and S2 are moving with the same speed. d) The kinetic energies of the two satellites are equal. Correct answer is option 'C'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Two satellites of earth, S1 and S2, are moving in the same orbit. The mass of S1 is four times the mass of S2. Which one of the following statements is true?a) The time period of S1 is four times that of S2. b) The potential energies of earth and satellite in the two cases are equal. c) S1 and S2 are moving with the same speed. d) The kinetic energies of the two satellites are equal. Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two satellites of earth, S1 and S2, are moving in the same orbit. The mass of S1 is four times the mass of S2. Which one of the following statements is true?a) The time period of S1 is four times that of S2. b) The potential energies of earth and satellite in the two cases are equal. c) S1 and S2 are moving with the same speed. d) The kinetic energies of the two satellites are equal. Correct answer is option 'C'. Can you explain this answer?.
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