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

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

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 –

Choices

Choice (4)Response

a.

b.

c.

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

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

Classical Mechanics

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

a.

b.

c.

d.

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