Classical Mechanics-Lagrange's and Hamilton's Formalisms (GATE (Graduate Aptitude Test in Engineering) Physics): Questions 5 - 8 of 21

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Question number: 5

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

Appeared in Year: 2016

MCQ▾

Question

The Lagrangian of a system is given by

, where are constants.

Which of the following is conserved?

Choices

Choice (4) Response

a.

b.

c.

d.

Passage

A particle of mass slides under the gravity without friction along the parabolic path , as shown in the figure. Here, is a constant.

Arc c Arc c: CircularArc [E, F, G] Vector u Vector u: Vector [A, B] Vector u Vector u: Vector [A, B] Vector v Vector v: Vector [C, D] Vector v Vector v: Vector [C, D] Vector w Vector w: Vector [H, I] Vector w Vector w: Vector [H, I] Vector a Vector a: Vector [J, K] Vector a Vector a: Vector [J, K] Point H H = (6.16,0.92) Point H H = (6.16,0.92) Y text1 = “Y”m text1_1 = “m”X text1_2 = “X”g text1_3 = “g”

a Particle Is Sliding Along the Parabolic Path

In a figure a particle of mass m slides under the gravity without friction along the parabolic path.

Question number: 6 (1 of 2 Based on Passage) Show Passage

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

Appeared in Year: 2012

MCQ▾

Question

The Lagrange’s equation of motion of the particle is –

Choices

Choice (4) Response

a.

b.

c.

d.

Question number: 7 (2 of 2 Based on Passage) Show Passage

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

Appeared in Year: 2012

MCQ▾

Question

The Lagrangian for this particle is given by –

Choices

Choice (4) Response

a.

b.

c.

d.

Question number: 8

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

Appeared in Year: 2013

MCQ▾

Question

The Lagrangian of a system with one degree of freedom is given by , where and are non –zero constants. If denotes the canonical momentum conjugate to then which one of the following statements is CORRECT?

Choices

Choice (4) Response

a.

and it is a conserved quantity

b.

and it is not a conserved quantity

c.

and it is not a conserved quantity

d.

and it is a conserved quantity

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