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

Appeared in Year: *2015*

### Question MCQ▾

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. | The total energy and total momentum are conserved | |

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

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

d. | Only the total energy is conserved |

## Answer

b.

## 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.

Ques. Time: