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Two satellites of same mass m are revolving round of earth (mass M) in the same orbit of radius r. Rotational directions of the two are opposite, therefore, they can collide. Total mechanical energy of the system is A) -(GMm)/r B) -(2GMm)/r C) -(GMm)/2r D) zero?
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Two satellites of same mass m are revolving round of earth (mass M) in...
Answer:
Given: Two satellites of same mass m are revolving round of earth (mass M) in the same orbit of radius r.
To find: Total mechanical energy of the system.
Solution:
Explanation:
When two satellites of equal mass are revolving in the same orbit of radius r and in opposite directions, then the relative speed of the two satellites is equal to the sum of their individual speeds, which is twice the speed of each satellite.
The centrifugal force acting on each satellite is given by:
F = mv²/r
where m is the mass of each satellite, v is the speed of each satellite, and r is the radius of the orbit.
The gravitational force between the two satellites is given by:
F = Gm²/r²
where G is the gravitational constant.
Since the two satellites are revolving in opposite directions, the gravitational force between them is attractive and the centrifugal force is repulsive. Therefore, the net force between the two satellites is:
F = Gm²/r² - 2mv²/r
The total mechanical energy of the system is given by the sum of the kinetic and potential energies of the two satellites:
E = 2(1/2mv²) - GmM/r
where M is the mass of the earth.
Substituting the expression for v² from the equation of motion:
v² = GM/r
where G is the gravitational constant and M is the mass of the earth.
We get:
E = -GMm/r - GMm/r
E = -2GMm/r
Therefore, the total mechanical energy of the system is -2GMm/r.
Answer: Option B) -(2GMm)/r
Given: Two satellites of same mass m are revolving round of earth (mass M) in the same orbit of radius r.
To find: Total mechanical energy of the system.
Solution:
Explanation:
When two satellites of equal mass are revolving in the same orbit of radius r and in opposite directions, then the relative speed of the two satellites is equal to the sum of their individual speeds, which is twice the speed of each satellite.
The centrifugal force acting on each satellite is given by:
F = mv²/r
where m is the mass of each satellite, v is the speed of each satellite, and r is the radius of the orbit.
The gravitational force between the two satellites is given by:
F = Gm²/r²
where G is the gravitational constant.
Since the two satellites are revolving in opposite directions, the gravitational force between them is attractive and the centrifugal force is repulsive. Therefore, the net force between the two satellites is:
F = Gm²/r² - 2mv²/r
The total mechanical energy of the system is given by the sum of the kinetic and potential energies of the two satellites:
E = 2(1/2mv²) - GmM/r
where M is the mass of the earth.
Substituting the expression for v² from the equation of motion:
v² = GM/r
where G is the gravitational constant and M is the mass of the earth.
We get:
E = -GMm/r - GMm/r
E = -2GMm/r
Therefore, the total mechanical energy of the system is -2GMm/r.
Answer: Option B) -(2GMm)/r
Community Answer
Two satellites of same mass m are revolving round of earth (mass M) in...
TE=ke+pe -GMM/2r+GMM/r=-GMM/2r for two satellite 2*-GMM/2r=-GMM/r
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Two satellites of same mass m are revolving round of earth (mass M) in the same orbit of radius r. Rotational directions of the two are opposite, therefore, they can collide. Total mechanical energy of the system is A) -(GMm)/r B) -(2GMm)/r C) -(GMm)/2r D) zero?
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Two satellites of same mass m are revolving round of earth (mass M) in the same orbit of radius r. Rotational directions of the two are opposite, therefore, they can collide. Total mechanical energy of the system is A) -(GMm)/r B) -(2GMm)/r C) -(GMm)/2r D) zero? 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 same mass m are revolving round of earth (mass M) in the same orbit of radius r. Rotational directions of the two are opposite, therefore, they can collide. Total mechanical energy of the system is A) -(GMm)/r B) -(2GMm)/r C) -(GMm)/2r D) zero? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two satellites of same mass m are revolving round of earth (mass M) in the same orbit of radius r. Rotational directions of the two are opposite, therefore, they can collide. Total mechanical energy of the system is A) -(GMm)/r B) -(2GMm)/r C) -(GMm)/2r D) zero?.
Two satellites of same mass m are revolving round of earth (mass M) in the same orbit of radius r. Rotational directions of the two are opposite, therefore, they can collide. Total mechanical energy of the system is A) -(GMm)/r B) -(2GMm)/r C) -(GMm)/2r D) zero? 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 same mass m are revolving round of earth (mass M) in the same orbit of radius r. Rotational directions of the two are opposite, therefore, they can collide. Total mechanical energy of the system is A) -(GMm)/r B) -(2GMm)/r C) -(GMm)/2r D) zero? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two satellites of same mass m are revolving round of earth (mass M) in the same orbit of radius r. Rotational directions of the two are opposite, therefore, they can collide. Total mechanical energy of the system is A) -(GMm)/r B) -(2GMm)/r C) -(GMm)/2r D) zero?.
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Two satellites of same mass m are revolving round of earth (mass M) in the same orbit of radius r. Rotational directions of the two are opposite, therefore, they can collide. Total mechanical energy of the system is A) -(GMm)/r B) -(2GMm)/r C) -(GMm)/2r D) zero?, a detailed solution for Two satellites of same mass m are revolving round of earth (mass M) in the same orbit of radius r. Rotational directions of the two are opposite, therefore, they can collide. Total mechanical energy of the system is A) -(GMm)/r B) -(2GMm)/r C) -(GMm)/2r D) zero? has been provided alongside types of Two satellites of same mass m are revolving round of earth (mass M) in the same orbit of radius r. Rotational directions of the two are opposite, therefore, they can collide. Total mechanical energy of the system is A) -(GMm)/r B) -(2GMm)/r C) -(GMm)/2r D) zero? theory, EduRev gives you an
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