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An object of mass m is fixed to a massless rod pivoted at point 'B'. The rod is free to move in any direction without any resistance. A large mass M is fixed to the point A. If the two masses interact with each other via gravity then the general motion of the system will satisfy the condition considering the conservation of it's angular momentum and energy conservation?
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An object of mass m is fixed to a massless rod pivoted at point 'B'. T...
Conservation of Angular Momentum and Energy in the System:
- Initial State:
In the initial state, the masses m and M are at rest and the system is stationary. The point A is at a distance r from the pivot point B.
- Angular Momentum Conservation:
When the system is set into motion, the angular momentum of the system about point B is conserved. The angular momentum of the system is given by L = Iω, where I is the moment of inertia and ω is the angular velocity.
- Energy Conservation:
The potential energy of the system due to the gravitational interaction between the masses m and M will get converted into kinetic energy as the system moves. The total energy of the system remains constant if we neglect any external forces.
- General Motion of the System:
As the masses m and M interact via gravity, they will start to move towards each other. The rod will rotate about the pivot point B due to the change in the distribution of mass. The system will continue to move until the masses come into contact or a new equilibrium is reached.
- Final State:
In the final state, the masses m and M may collide or reach a new equilibrium position where the forces due to gravity and the rod's rotation are balanced.
Therefore, by considering the conservation of angular momentum and energy in the system, we can predict the general motion of the masses m and M attached to the massless rod pivoted at point B.
- Initial State:
In the initial state, the masses m and M are at rest and the system is stationary. The point A is at a distance r from the pivot point B.
- Angular Momentum Conservation:
When the system is set into motion, the angular momentum of the system about point B is conserved. The angular momentum of the system is given by L = Iω, where I is the moment of inertia and ω is the angular velocity.
- Energy Conservation:
The potential energy of the system due to the gravitational interaction between the masses m and M will get converted into kinetic energy as the system moves. The total energy of the system remains constant if we neglect any external forces.
- General Motion of the System:
As the masses m and M interact via gravity, they will start to move towards each other. The rod will rotate about the pivot point B due to the change in the distribution of mass. The system will continue to move until the masses come into contact or a new equilibrium is reached.
- Final State:
In the final state, the masses m and M may collide or reach a new equilibrium position where the forces due to gravity and the rod's rotation are balanced.
Therefore, by considering the conservation of angular momentum and energy in the system, we can predict the general motion of the masses m and M attached to the massless rod pivoted at point B.
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An object of mass m is fixed to a massless rod pivoted at point 'B'. The rod is free to move in any direction without any resistance. A large mass M is fixed to the point A. If the two masses interact with each other via gravity then the general motion of the system will satisfy the condition considering the conservation of it's angular momentum and energy conservation?
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An object of mass m is fixed to a massless rod pivoted at point 'B'. The rod is free to move in any direction without any resistance. A large mass M is fixed to the point A. If the two masses interact with each other via gravity then the general motion of the system will satisfy the condition considering the conservation of it's angular momentum and energy conservation? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about An object of mass m is fixed to a massless rod pivoted at point 'B'. The rod is free to move in any direction without any resistance. A large mass M is fixed to the point A. If the two masses interact with each other via gravity then the general motion of the system will satisfy the condition considering the conservation of it's angular momentum and energy conservation? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An object of mass m is fixed to a massless rod pivoted at point 'B'. The rod is free to move in any direction without any resistance. A large mass M is fixed to the point A. If the two masses interact with each other via gravity then the general motion of the system will satisfy the condition considering the conservation of it's angular momentum and energy conservation?.
An object of mass m is fixed to a massless rod pivoted at point 'B'. The rod is free to move in any direction without any resistance. A large mass M is fixed to the point A. If the two masses interact with each other via gravity then the general motion of the system will satisfy the condition considering the conservation of it's angular momentum and energy conservation? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about An object of mass m is fixed to a massless rod pivoted at point 'B'. The rod is free to move in any direction without any resistance. A large mass M is fixed to the point A. If the two masses interact with each other via gravity then the general motion of the system will satisfy the condition considering the conservation of it's angular momentum and energy conservation? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An object of mass m is fixed to a massless rod pivoted at point 'B'. The rod is free to move in any direction without any resistance. A large mass M is fixed to the point A. If the two masses interact with each other via gravity then the general motion of the system will satisfy the condition considering the conservation of it's angular momentum and energy conservation?.
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