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Two satellites of earth, S1 and S2 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 of period 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 moving in the same orbit. The mass ...
Explanation:
When two satellites are moving in the same orbit, they have the same orbital speed. This is because the centripetal force required to keep the satellites in orbit is provided by the gravitational force, which is the same for both satellites. Therefore, option (c) is correct.
To understand why option (a) is incorrect, let's consider the formula for the period of an orbiting satellite:
T = 2π√(r³/GM)
where T is the period, r is the radius of the orbit, G is the gravitational constant, and M is the mass of the central body (in this case, Earth).
Since both satellites are moving in the same orbit, they have the same radius (r) and the same gravitational constant (G). The only difference is the mass of the satellites (M1 and M2).
If the mass of S1 is four times the mass of S2 (M1 = 4M2), we can substitute these values into the formula:
T1 = 2π√(r³/G(4M2)) = 2π√(r³/GM2) = 2π√(r³/GM) = T2
As we can see, the periods of the two satellites are the same. Therefore, option (a) is incorrect.
To understand why option (b) is incorrect, we need to consider the formula for the potential energy of an object in orbit:
PE = -GMm/r
where PE is the potential energy, G is the gravitational constant, M is the mass of the central body (Earth), m is the mass of the satellite, and r is the radius of the orbit.
The potential energy depends on the mass of the satellite (m), which is different for S1 and S2. Therefore, the potential energies of the Earth and the satellites are not equal. Hence, option (b) is incorrect.
Finally, the kinetic energy of a satellite is given by the formula:
KE = (1/2)mv²
where KE is the kinetic energy, m is the mass of the satellite, and v is the orbital speed.
Since both satellites are moving in the same orbit, they have the same orbital speed (v). The only difference is the mass of the satellites (m1 and m2).
If the mass of S1 is four times the mass of S2 (m1 = 4m2), we can substitute these values into the formula:
KE1 = (1/2)(4m2)v² = 2(1/2)m2v² = (1/2)m2v² = KE2
As we can see, the kinetic energies of the two satellites are equal. Therefore, option (d) is incorrect.
When two satellites are moving in the same orbit, they have the same orbital speed. This is because the centripetal force required to keep the satellites in orbit is provided by the gravitational force, which is the same for both satellites. Therefore, option (c) is correct.
To understand why option (a) is incorrect, let's consider the formula for the period of an orbiting satellite:
T = 2π√(r³/GM)
where T is the period, r is the radius of the orbit, G is the gravitational constant, and M is the mass of the central body (in this case, Earth).
Since both satellites are moving in the same orbit, they have the same radius (r) and the same gravitational constant (G). The only difference is the mass of the satellites (M1 and M2).
If the mass of S1 is four times the mass of S2 (M1 = 4M2), we can substitute these values into the formula:
T1 = 2π√(r³/G(4M2)) = 2π√(r³/GM2) = 2π√(r³/GM) = T2
As we can see, the periods of the two satellites are the same. Therefore, option (a) is incorrect.
To understand why option (b) is incorrect, we need to consider the formula for the potential energy of an object in orbit:
PE = -GMm/r
where PE is the potential energy, G is the gravitational constant, M is the mass of the central body (Earth), m is the mass of the satellite, and r is the radius of the orbit.
The potential energy depends on the mass of the satellite (m), which is different for S1 and S2. Therefore, the potential energies of the Earth and the satellites are not equal. Hence, option (b) is incorrect.
Finally, the kinetic energy of a satellite is given by the formula:
KE = (1/2)mv²
where KE is the kinetic energy, m is the mass of the satellite, and v is the orbital speed.
Since both satellites are moving in the same orbit, they have the same orbital speed (v). The only difference is the mass of the satellites (m1 and m2).
If the mass of S1 is four times the mass of S2 (m1 = 4m2), we can substitute these values into the formula:
KE1 = (1/2)(4m2)v² = 2(1/2)m2v² = (1/2)m2v² = KE2
As we can see, the kinetic energies of the two satellites are equal. Therefore, option (d) is incorrect.
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Two satellites of earth, S1 and S2 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 of period S1 is four times that of S2b)The potential energies of earth and satellite in the two cases are equalc)S1 and S2 are moving with the same speedd)The kinetic energies of the two satellites are equalCorrect answer is option 'C'. Can you explain this answer?
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Two satellites of earth, S1 and S2 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 of period S1 is four times that of S2b)The potential energies of earth and satellite in the two cases are equalc)S1 and S2 are moving with the same speedd)The kinetic energies of the two satellites are equalCorrect answer is option 'C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Two satellites of earth, S1 and S2 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 of period S1 is four times that of S2b)The potential energies of earth and satellite in the two cases are equalc)S1 and S2 are moving with the same speedd)The kinetic energies of the two satellites are equalCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two satellites of earth, S1 and S2 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 of period S1 is four times that of S2b)The potential energies of earth and satellite in the two cases are equalc)S1 and S2 are moving with the same speedd)The kinetic energies of the two satellites are equalCorrect answer is option 'C'. Can you explain this answer?.
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