Classical Mechanics-Lagrange's and Hamilton's Formalisms (GATE Physics): Questions 4 - 4 of 8

Get 1 year subscription: Access detailed explanations (illustrated with images and videos) to 290 questions. Access all new questions we will add tracking exam-pattern and syllabus changes. View Sample Explanation or View Features.

Rs. 200.00 or

Question number: 4

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

Appeared in Year: 2012

MCQ▾

Question

A particle of mass m is attached to a fixed point O by a weightless inextensible string of length a . 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,

L(θ,ϕ)=12ma2(θ˙2+sin2θϕ˙2)mgacosθ

Where, θ and ϕ are the polar angles.

The Hamiltonian of the particle is,

Choices

Choice (4) Response

a.

H=12ma2(pθ2+pϕ2sin2θ)mgacosθ

b.

H=12ma2(pθ2+pϕ2)+mgacosθ

c.

H=12ma2(pθ2+pϕ2)mgacosθ

d.

H=12ma2(pθ2+pϕ2sin2θ)+mgacosθ

Sign In