Classical Mechanics-Lagrange's and Hamilton's Formalisms (GATE (Graduate Aptitude Test in Engineering) Physics): Questions 1 - 3 of 21

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Question number: 1

» Classical Mechanics » Lagrange's and Hamilton's Formalisms

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Appeared in Year: 2015

MCQ▾

Question

The Hamiltonian for a system of two particles of masses and at and having velocities and is given by , where C is a constant. Which one of the following statements is correct?

Choices

Choice (4) Response

a.

The total energy and total momentum are conserved

b.

The total energy and component of the total angular momentum are conserved

c.

The total energy and total angular momentum are conserved.

d.

Only the total energy is conserved

Question number: 2

» Classical Mechanics » Lagrange's and Hamilton's Formalisms

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Appeared in Year: 2014

MCQ▾

Question

The Hamilton’s canonical equations of motion in terms of Poisson Brackets are –

Choices

Choice (4) Response

a.

b.

c.

d.

Question number: 3

» Classical Mechanics » Lagrange's and Hamilton's Formalisms

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Appeared in Year: 2012

MCQ▾

Question

A particle of mass is attached to a fixed point by a weightless inextensible string of length . It is rotating under the gravity as shown in the figure.

Ellipse c Ellipse c: Ellipse with foci C, D passing through E Arc d Arc d: CircularArc [P, Q, R] Segment f Segment f: Segment [F, G] Segment g Segment g: Segment [H, I] Vector u Vector u: Vector [A, B] Vector u Vector u: Vector [A, B] Vector v Vector v: Vector [J, K] Vector v Vector v: Vector [J, K] Vector w Vector w: Vector [L, M] Vector w Vector w: Vector [L, M] Vector a Vector a: Vector [N, O] Vector a Vector a: Vector [N, O] Vector a Vector a: Vector [N, O] Point G Point G: Point on u Point G Point G: Point on u Point J Point J: Point on c Point J Point J: Point on c Point Q Q = (5.8,3.7) Point Q Q = (5.8,3.7) Point R R = (5.52,2.42) Point R R = (5.52,2.42) ? text1 = “? “ Z text1_1 = “Z” a text1_2 = “a” m text1_3 = “m” g text1_4 = “g” O text1_5 = “O”

A Particle Rotates About Z – Axis

In figure a particle of mass m, is attached to a fixed point O by a weightless inextensible string. And this particle rotating about Z – axis.

The Lagrangian of the particle is,

Where, and are the polar angles.

The Hamiltonian of the particle is,

Choices

Choice (4) Response

a.

b.

c.

d.

Developed by: