Classical Mechanics (CSIR Physical Sciences): Questions 10 - 12 of 55

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Question number: 10

» 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

Question number: 11

» 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: 12

» Classical Mechanics » Special Theory of Relativity » Mass-Energy Equivalence

Appeared in Year: 2012

MCQ▾

Question

Three particle of equal mass m are connected by two identical mass less springs of stiffness constant k as shown in figure –

A system of three particles and two springs

A System of Three Particles and Two Springs

In figure three particles of equal mass m are connected by two identical massless springs of stiffness constant k.

If x1,x2andx3 denote the horizontal displacements of the masses from their respective equilibrium position, the potential energy of the system is – (December)

Choices

Choice (4) Response
a.

12k[x12+x22+x32x2(x1+x3)]

b.

12k[x12+2x22+x32+2x2(x1+x3)]

c.

12k[x12+x22+x32]

d.

12k[x12+2x22+x322x2(x1+x3)]

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