Classical Mechanics-Lagrange's and Hamilton's Formalisms (GATE Physics): Questions 4 - 4 of 20

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Question number: 4

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

Appeared in Year: 2012

MCQ▾

Question

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

Ellipse c Ellipse c: Ellipse with foci C, D passing through EArc 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 uPoint G Point G: Point on uPoint J Point J: Point on cPoint J Point J: Point on cPoint 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,

Equation

Where, Equation and Equation are the polar angles.

The Hamiltonian of the particle is,

Choices

Choice (4) Response

a.

Equation

b.

Equation

c.

Equation

d.

Equation

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