# Classical Mechanics [GATE (Graduate Aptitude Test in Engineering) Physics]: Questions 59 - 63 of 84

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## Question 59

Appeared in Year: *2007*

### Question

MCQ▾The Hamiltonian of a particle is , where is the generalized coordinate and is the corresponding canonical momentum. The Lagrangian is –

### Choices

Choice (4) | Response | |
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a. | ||

b. | ||

c. | ||

d. |

## Question 60

Appeared in Year: *2008*

### Question

MCQ▾A hoop of radius is pivoted at a point on the circumference. The period of small oscillations in the plane of the hoop is –

### Choices

Choice (4) | Response | |
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a. | ||

b. | ||

c. | ||

d. |

## Question 61

Appeared in Year: *2007*

### Question

MCQ▾For a particle of mass in a one – dimensional harmonic oscillator potential of the form , the first excited energy eigenstate is . The value of is –

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Choice (4) | Response | |
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d. |

## Question 62

Appeared in Year: *2007*

### Question

MCQ▾The Lagrangian of a particle of mass is

, where and are constants. The conserved quantities are –

### Choices

Choice (4) | Response | |
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a. | Energy and – components of both linear and angular momenta. | |

b. | Energy and component of angular momentum only. | |

c. | Energy and – component of linear momentum only. | |

d. | components of both linear and angular momenta only. |

## Question 63

Appeared in Year: *2008*

### Question

MCQ▾A rigid body is rotating about its centre of mass, fixed at the origin, with an angular velocity and angular acceleration . If the torque acting on it is and its angular momentum is , the rate of change of its kinetic energy is –

### Choices

Choice (4) | Response | |
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a. | ||

b. | ||

c. | ||

d. |