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If the gravitational force between two objects were proportional to 1/R (and not as 1/R2) where R is separation between them, then a particle in circular orbit under such a force would have its orbital speed v proportional to [1989]
- a)1/R2
- b)R0
- c)R1
- d)1/R
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
If the gravitational force between two objects were proportional to 1/...
Hence v ∝ R0Most Upvoted Answer
If the gravitational force between two objects were proportional to 1/...
Explanation:
In a circular orbit, the centripetal force acting on a particle is provided by the gravitational force between the two objects.
Gravitational force:
According to Newton's law of gravitation, the gravitational force between two objects is given by:
F = G * (m1 * m2) / R^2
where F is the gravitational force, G is the gravitational constant, m1 and m2 are the masses of the two objects, and R is the separation between them.
In this case, the gravitational force is proportional to 1/R instead of 1/R^2. So, the force equation becomes:
F = k * (m1 * m2) / R
where k is a constant of proportionality.
Centripetal force:
In a circular orbit, the centripetal force required to keep the particle in circular motion is given by:
F = (m * v^2) / R
where F is the centripetal force, m is the mass of the particle, v is the orbital speed, and R is the radius of the circular orbit.
Equating the gravitational force and centripetal force:
Setting the gravitational force equal to the centripetal force, we have:
k * (m1 * m2) / R = (m * v^2) / R
Simplifying the equation, we get:
k * (m1 * m2) = m * v^2
Relationship between orbital speed and separation:
From the equation above, we can see that the orbital speed, v, is independent of the separation, R. This means that the orbital speed is constant regardless of the distance between the two objects. Therefore, the orbital speed, v, is proportional to R^0.
Hence, the correct answer is option 'B' - R^0.
In a circular orbit, the centripetal force acting on a particle is provided by the gravitational force between the two objects.
Gravitational force:
According to Newton's law of gravitation, the gravitational force between two objects is given by:
F = G * (m1 * m2) / R^2
where F is the gravitational force, G is the gravitational constant, m1 and m2 are the masses of the two objects, and R is the separation between them.
In this case, the gravitational force is proportional to 1/R instead of 1/R^2. So, the force equation becomes:
F = k * (m1 * m2) / R
where k is a constant of proportionality.
Centripetal force:
In a circular orbit, the centripetal force required to keep the particle in circular motion is given by:
F = (m * v^2) / R
where F is the centripetal force, m is the mass of the particle, v is the orbital speed, and R is the radius of the circular orbit.
Equating the gravitational force and centripetal force:
Setting the gravitational force equal to the centripetal force, we have:
k * (m1 * m2) / R = (m * v^2) / R
Simplifying the equation, we get:
k * (m1 * m2) = m * v^2
Relationship between orbital speed and separation:
From the equation above, we can see that the orbital speed, v, is independent of the separation, R. This means that the orbital speed is constant regardless of the distance between the two objects. Therefore, the orbital speed, v, is proportional to R^0.
Hence, the correct answer is option 'B' - R^0.
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If the gravitational force between two objects were proportional to 1/R (and not as 1/R2) where R is separation between them, then a particle in circular orbit under such a force would have its orbital speed v proportional to [1989]a)1/R2b)R0c)R1d)1/RCorrect answer is option 'B'. Can you explain this answer? for NEET 2025 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about If the gravitational force between two objects were proportional to 1/R (and not as 1/R2) where R is separation between them, then a particle in circular orbit under such a force would have its orbital speed v proportional to [1989]a)1/R2b)R0c)R1d)1/RCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for NEET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the gravitational force between two objects were proportional to 1/R (and not as 1/R2) where R is separation between them, then a particle in circular orbit under such a force would have its orbital speed v proportional to [1989]a)1/R2b)R0c)R1d)1/RCorrect answer is option 'B'. Can you explain this answer?.
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