Classical Mechanics-Lagrangian and Hamiltonian Formalism and Equations of Motion (CSIR Physical Sciences): Questions 1 - 3 of 11

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Question number: 1

» Classical Mechanics » Lagrangian and Hamiltonian Formalism and Equations of Motion

Appeared in Year: 2013

MCQ▾

Question

The Hamiltonian of a relativistic particle of rest mass m and momentum p is given by H=p2+m2+V(x) , in units in which the speed of light c=1 . The corresponding Lagrangian is – (December)

Choices

Choice (4) Response

a.

L=m1x˙2V(x)

b.

L=12mx˙2V(x)

c.

L=m1+x˙2V(x)

d.

L=1+mx˙2V(x)

Question number: 2

» Classical Mechanics » Lagrangian and Hamiltonian Formalism and Equations of Motion

Appeared in Year: 2013

MCQ▾

Question

The Lagrangian of a particle of mass m moving in one dimension is given by,

L=12mx˙2bx

Where, b is a positive constant. The coordinate of the particle x(t) at time t is given by: (in the following c1 and c2 are constants) (June)

Choices

Choice (4) Response

a.

c1t+c2

b.

b2mt2+c1t+c2

c.

c1cos(btm)+c2sin(btm)

d.

c1cosh(btm)+c2sinh(btm)

Question number: 3

» Classical Mechanics » Lagrangian and Hamiltonian Formalism and Equations of Motion

Appeared in Year: 2014

MCQ▾

Question

A particle of mass m and coordinate q has the Lagrangian L=12mq˙2λ2qq˙2 ; where λ is a constant. The Hamiltonian for the system is given by, (June)

Choices

Choice (4) Response

a.

p22m+λqp22(mλq)2

b.

p22(mλq)

c.

p22m+λqp22m2

d.

pq˙2

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