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A particle of mass m moves under the influence of a central force given by F(r) = where r is the distance of the particle from the center of the force, and k is a constant. The particle is released from rest at a distance R from the center of the force. What is the maximum speed attained by the particle as it moves towards the center of the force?
  • a)
  • b)
  • c)
  • d)
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
A particle of mass m moves under the influence of a central force give...
We can use conservation of energy to find the maximum speed attained by the particle.
Since the particle is released from rest, its initial kinetic energy is zero, and its potential energy at any position is given by:

Solving above we get:

At any point along its trajectory, the total energy of the particle is given by:

where v is the speed of the particle and r is its distance from the center of the force.
At the point of maximum speed, the kinetic energy of the particle is equal to its total energy, so:
Solving this we will get:
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A particle of mass m moves under the influence of a central force given by F(r) =where r is the distance of the particle from the center of the force, and k is a constant. The particle is released from rest at a distance R from the center of the force. What is the maximum speed attained by the particle as it moves towards the center of the force?a)b)c)d)Correct answer is option 'B'. Can you explain this answer?
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A particle of mass m moves under the influence of a central force given by F(r) =where r is the distance of the particle from the center of the force, and k is a constant. The particle is released from rest at a distance R from the center of the force. What is the maximum speed attained by the particle as it moves towards the center of the force?a)b)c)d)Correct answer is option 'B'. Can you explain this answer? for UGC NET 2024 is part of UGC NET preparation. The Question and answers have been prepared according to the UGC NET exam syllabus. Information about A particle of mass m moves under the influence of a central force given by F(r) =where r is the distance of the particle from the center of the force, and k is a constant. The particle is released from rest at a distance R from the center of the force. What is the maximum speed attained by the particle as it moves towards the center of the force?a)b)c)d)Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for UGC NET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle of mass m moves under the influence of a central force given by F(r) =where r is the distance of the particle from the center of the force, and k is a constant. The particle is released from rest at a distance R from the center of the force. What is the maximum speed attained by the particle as it moves towards the center of the force?a)b)c)d)Correct answer is option 'B'. Can you explain this answer?.
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