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A bead of mass m can slide without friction along a massless rod kept at 45° with the vertical as shown in the figure. The rod is rotating about the vertical axis with a constant angular speed ω. At any instant r is the distance of the bead from the origin. The momentum conjugate to r is?
  • a)
    mr
  • b)
  • c)
  • d)
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
A bead of mass m can slide without friction along a massless rod kept ...
The conjugate momentum is given by

where L is the Lagrangian of the system.
Calculation:
The Lagrangian for the system is written as:

The equation of constrain is θ = π/4 and it is given ϕ̇ = ω

Thus, the momentum conjugate to r is 
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A bead of mass m can slide without friction along a massless rod kept at 45° with the vertical as shown in the figure. The rod is rotating about the vertical axis with a constant angular speed ω. At any instant r is the distance of the bead from the origin. The momentum conjugate to r is?a)mrb)c)d)Correct answer is option 'A'. Can you explain this answer?
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