# Classical Mechanics [GATE (Graduate Aptitude Test in Engineering) Physics]: Questions 48 - 54 of 84

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### Passage

A particle of mass is constrained to move in a vertical plane along a trajectory given by , where is a constant.

## Question 48 (1 of 2 Based on Passage)

Appeared in Year: *2006*

### Question

MCQ▾The equation of motion of the particle is –

### Choices

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

b. | ||

c. | ||

d. |

## Question 49 (2 of 2 Based on Passage)

Appeared in Year: *2006*

### Question

MCQ▾The Lagrangian of the particle is –

### Choices

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

b. | ||

c. | ||

d. |

### Passage

In the laboratory frame, a particle of rest mass is moving in the positive direction with a speed of . It approaches an identical particle , moving in the negative direction with a speed of .

## Question 50 (1 of 2 Based on Passage)

Appeared in Year: *2007*

### Question

MCQ▾The speed of the particle in the rest frame of the particle is –

### Choices

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

b. | ||

c. | ||

d. |

## Question 51 (2 of 2 Based on Passage)

Appeared in Year: *2007*

### Question

MCQ▾The energy of the particle in the rest frame of the particle is –

### Choices

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

b. | ||

c. | ||

d. |

## Question 52

Appeared in Year: *2008*

### Question

MCQ▾For a simple harmonic oscillator the Lagrangian is given by . If and is the Hamiltonian of the system, the Poisson bracket is given by –

### Choices

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

b. | ||

c. | ||

d. |

## Question 53

Appeared in Year: *2007*

### Question

MCQ▾A space station moving in a circular around the Earth goes into a new bound orbit by firing its engine radially outwards. This orbit is –

### Choices

Choice (4) | Response | |
---|---|---|

a. | A smaller circle | |

b. | An ellipse | |

c. | A parabola | |

d. | A larger circle |

## Question 54

Appeared in Year: *2008*

### Question

MCQ▾An inelastic ball of mass has been thrown vertically upward from the ground at . The initial kinetic energy of ball is . The phase trajectory of the ball after successive bouncing on the ground is –

### Choices

Choice (4) | Response | |
---|---|---|

a. | ||

b. | ||

c. | ||

d. |