Classical Mechanics (CSIR Physical Sciences): Questions 1 - 4 of 59

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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 » Rigid Body Dynamics - Moment of Inertia Tensor

Appeared in Year: 2013

MCQ▾

Question

A uniform cylinder of radius r and length l and a uniform sphere of radius R are released on an inclined plane when their centers of mass are at same height. If they roll down without slipping and if the sphere reaches the bottom of plane with a speed V, then the speed of the cylinder when it reaches the bottom is: (June)

Choices

Choice (4) Response

a.

V1415

b.

4Vr15R

c.

V14rl15R2

d.

4V15

Question number: 3

» Classical Mechanics » Poisson Brackets

Appeared in Year: 2013

MCQ▾

Question

Let A, B and C be function of phase space variables (coordinates and momenta of a mechanical system). If {, } represents the Poisson bracket, the value of {A,{B,C}}{{A,B},C} is given by – (December)

Choices

Choice (4) Response

a.

{B,{C,A}}

b.

{{C,A},B}

c.

{A,{C,B}}

d.

0

Question number: 4

» 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)

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