# 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

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

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)

Classical Mechanics

Appeared in Year: 2007

### Question

MCQ▾

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

### Choices

Choice (4)Response

a.

b.

c.

d.

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

Classical Mechanics

Appeared in Year: 2007

### Question

MCQ▾

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

### Choices

Choice (4)Response

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

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.

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