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 

b.  The total energy and total momentum are conserved 

c.  The total energy and total angular momentum are conserved. 

d.  The total energy and component of the total angular momentum are conserved 

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Answer
Explanation

Here, the Hamiltonian for a system of two particles of masses and at and having velocities and is given as,

Comparing above equation with standard operator, that is given as,

Only z – component of angular momentum is associated. Therefore, the total energy as well as z – component of the total angular momentum are conserved.