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A particle of mass m is attached to a fixed point O by a weightless inextensible string of length a. It is rotating under the gravity as shown in the figure. The Lagrangian of the particle is  − mga cos θ where θ and ϕ are the polar angles. The Hamiltonian of the particles is
  • a)
  • b)
  • c)
  • d)
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
A particle of mass m is attached to a fixed point O by a weightless in...
Concept:
The Hamiltonian of a system specifies its total energy—
i.e., the sum of its kinetic energy and its potential energy—in terms of the Lagrangian function.
Calculation:

Put the value of θ˙ and ϕ˙
 
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A particle of mass m is attached to a fixed point O by a weightless inextensible string of length a. It is rotating under the gravity as shown in the figure. The Lagrangian of the particle is− mgacos θ where θ and are the polar angles. The Hamiltonian of the particles isa)b)c)d)Correct answer is option 'B'. Can you explain this answer?
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A particle of mass m is attached to a fixed point O by a weightless inextensible string of length a. It is rotating under the gravity as shown in the figure. The Lagrangian of the particle is− mgacos θ where θ and are the polar angles. The Hamiltonian of the particles isa)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 is attached to a fixed point O by a weightless inextensible string of length a. It is rotating under the gravity as shown in the figure. The Lagrangian of the particle is− mgacos θ where θ and are the polar angles. The Hamiltonian of the particles isa)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 is attached to a fixed point O by a weightless inextensible string of length a. It is rotating under the gravity as shown in the figure. The Lagrangian of the particle is− mgacos θ where θ and are the polar angles. The Hamiltonian of the particles isa)b)c)d)Correct answer is option 'B'. Can you explain this answer?.
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