Classical Mechanics-Lagrange's and Hamilton's Formalisms (GATE (Graduate Aptitude Test in Engineering) Physics): Questions 5 - 8 of 20

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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

Equation , where Equation are constants.

Which of the following is conserved?

Choices

Choice (4) Response

a.

Equation

b.

Equation

c.

Equation

d.

Equation

Passage

A particle of mass Equation slides under the gravity without friction along the parabolic path Equation , as shown in the figure. Here, Equation 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 Lagrangian for this particle is given by –

Choices

Choice (4) Response

a.

Equation

b.

Equation

c.

Equation

d.

Equation

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 Lagrange’s equation of motion of the particle is –

Choices

Choice (4) Response

a.

Equation

b.

Equation

c.

Equation

d.

Equation

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 Equation is given by Equation , where Equation and Equation are non –zero constants. If Equation denotes the canonical momentum conjugate to Equation then which one of the following statements is CORRECT?

Choices

Choice (4) Response

a.

Equation and it is a conserved quantity

b.

Equation and it is not a conserved quantity

c.

Equation and it is not a conserved quantity

d.

Equation and it is a conserved quantity

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