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A particle moves in a circular orbit under the action of a central attractive force inversely proportional to the distance 'r'. The speed of the particle is
- a)Proportional to r2
- b)Independent of r
- c)Proportional to r
- d)Proportional to 1/r
Correct answer is option 'B'. Can you explain this answer?
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A particle moves in a circular orbit under the action of a central att...
i.e. speed of the particle is independent of r
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A particle moves in a circular orbit under the action of a central att...
The motion of a particle in a circular orbit under the influence of a central attractive force can be described by the principles of circular motion and the law of universal gravitation. In this case, the central attractive force is inversely proportional to the distance between the particle and the center of the orbit.
The speed of the particle can be determined by considering the conservation of angular momentum. Angular momentum is given by the product of the moment of inertia and the angular velocity. In this case, the moment of inertia is proportional to the square of the distance from the center of the orbit, and the angular velocity is inversely proportional to the distance. Therefore, the angular momentum is constant.
Let's now consider the relationship between the speed of the particle and the distance from the center of the orbit:
1. The speed of the particle is inversely proportional to the distance from the center of the orbit. This is because as the particle moves further away from the center, the attractive force decreases, causing the particle to slow down.
2. The speed of the particle is independent of the distance from the center of the orbit. This is because the conservation of angular momentum ensures that the product of the moment of inertia and the angular velocity remains constant. Therefore, as the moment of inertia increases (proportional to r^2), the angular velocity decreases (inversely proportional to r) in such a way that the speed of the particle remains constant.
Therefore, the correct answer is option 'B': The speed of the particle is independent of r. This means that regardless of the distance from the center of the orbit, the particle will maintain a constant speed throughout its circular motion.
The speed of the particle can be determined by considering the conservation of angular momentum. Angular momentum is given by the product of the moment of inertia and the angular velocity. In this case, the moment of inertia is proportional to the square of the distance from the center of the orbit, and the angular velocity is inversely proportional to the distance. Therefore, the angular momentum is constant.
Let's now consider the relationship between the speed of the particle and the distance from the center of the orbit:
1. The speed of the particle is inversely proportional to the distance from the center of the orbit. This is because as the particle moves further away from the center, the attractive force decreases, causing the particle to slow down.
2. The speed of the particle is independent of the distance from the center of the orbit. This is because the conservation of angular momentum ensures that the product of the moment of inertia and the angular velocity remains constant. Therefore, as the moment of inertia increases (proportional to r^2), the angular velocity decreases (inversely proportional to r) in such a way that the speed of the particle remains constant.
Therefore, the correct answer is option 'B': The speed of the particle is independent of r. This means that regardless of the distance from the center of the orbit, the particle will maintain a constant speed throughout its circular motion.
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A particle moves in a circular orbit under the action of a central attractive force inversely proportional to the distance 'r'. The speed of the particle isa)Proportional to r2b)Independent of rc)Proportional to rd)Proportional to 1/rCorrect answer is option 'B'. Can you explain this answer?
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