# GATE (Graduate Aptitude Test in Engineering) Physics: Questions 1 of 659

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Appeared in Year: 2015

MCQ▾

### 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

Topic iScore

Ques. Time

d.

## 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.

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