Classical Mechanics-Lagrangian and Hamiltonian Formalism and Equations of Motion (CSIR Physical Sciences): Questions 4 - 7 of 11

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Question number: 4

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

Appeared in Year: 2012

MCQ▾

Question

If the Lagrangian of a particle moving in one dimension is given by L=x˙22xV(x), the Hamiltonian is – (June)

Choices

Choice (4) Response

a.

12xp2+V(x)

b.

12x˙2+V(x)

c.

x˙22x+V(x)

d.

p22x+V(x)

Question number: 5

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

Appeared in Year: 2014

MCQ▾

Question

The equation of motion of a system described by the time dependent Lagrangian L=eγt[12mx˙2V(x)] is – (December)

Choices

Choice (4) Response

a.

mx¨+γmx˙+dVdx=0

b.

mx¨+dVdx=0

c.

mx¨+γmx˙dVdx=0

d.

mx¨γmx˙+dVdx=0

Question number: 6

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

Appeared in Year: 2013

MCQ▾

Question

A system is governed by Hamiltonian,

H=12(pxay)2+12(pybx)2

Where a and b are constant are px,py are momenta conjugate to x and y respectively. For what value of a and b will the quantities (px3y) and (py+2x) be conserved? (June)

Choices

Choice (4) Response

a.

a=3,b=2

b.

a=3,b=2

c.

a=2,b=3

d.

a=2,b=3

Question number: 7

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

Appeared in Year: 2012

MCQ▾

Question

The Hamiltonian of a simple pendulum consisting of a mass m attached to a massless string of length l is H=pθ22ml2+mgl(1cosθ) . If L denotes the Lagrangian, the value of dLdt is – (December)

Choices

Choice (4) Response

a.

glpθcosθ

b.

2glpθsinθ

c.

glpθsin2θ

d.

lpθ2cosθ

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