Classical Mechanics-Lagrange's and Hamilton's Formalisms (GATE Physics): Questions 1 - 3 of 8

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Question number: 1

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

Appeared in Year: 2015

MCQ▾

Question

The Hamiltonian for a system of two particles of masses m1 and m2 at r1 and r2 having velocities v1 and v2 is given by H=12m1v12+12m2v22+C(r1r2)2z^(r1×r2) , where C is a constant. Which one of the following statements is correct?

Choices

Choice (4) Response

a.

Only the total energy is conserved

b.

The total energy and total momentum are conserved

c.

The total energy and total angular momentum are conserved.

d.

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

Question number: 2

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

Appeared in Year: 2015

MCQ▾

Question

The Lagrangian for a particle of mass m at a position r moving with a velocity v is given by L=m2v2+CrvV(r) , where V(r) is a potential and C is a constant. If pc is the canonical momentum, then its Hamiltonian is given by,

Choices

Choice (4) Response

a.

12m(pcCr)2+V(r)

b.

pc22m+V(r)

c.

12mpc2+C2r2+V(r)

d.

12m(pc+Cr)2+V(r)

Question number: 3

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

Appeared in Year: 2014

MCQ▾

Question

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

Choices

Choice (4) Response

a.

q˙={H,p};p˙={H.q}

b.

q˙={H,q};p˙={H,P}

c.

q˙={q,H};p˙={p.H}

d.

q˙={p,H};p˙={q,H}

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