GATE (Graduate Aptitude Test in Engineering) Physics: Questions 1 of 659
» Classical Mechanics » Lagrange's and Hamilton's Formalisms
Appeared in Year: 2015
Question
The Hamiltonian for a system of two particles of masses and at and having velocities and is given by , where C is a constant. Which one of the following statements is correct?
Choices
| Choice (4) | Response | |
|---|---|---|
| a. | Only the total energy is conserved |
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| b. | The total energy and total momentum are conserved |
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| c. | The total energy and total angular momentum are conserved. |
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| d. | The total energy and component of the total angular momentum are conserved |
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Answer
Explanation
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Here, the Hamiltonian for a system of two particles of masses and at and having velocities and is given as,
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Comparing above equation with standard operator, that is given as,
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Only z – component of angular momentum is associated. Therefore, the total energy as well as z – component of the total angular momentum are conserved.