Classical Mechanics-Lagrange's and Hamilton's Formalisms (GATE Physics): Questions 5 - 8 of 8

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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

L=12ml2[θ˙+sin2θφ˙]mglcosθ , where m,landg are constants.

Which of the following is conserved?

Choices

Choice (4) Response

a.

φ˙sin2θ

b.

φ˙sin2θ

c.

φ˙sinθ

d.

φ˙sinθ

Passage

A particle of mass m slides under the gravity without friction along the parabolic path y=ax2 , as shown in the figure. Here, a 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.

L=12mx˙2mgax2

b.

L=12m(1+4a2x2)x˙2mgax2

c.

L=12mx˙2+mgax2

d.

L=12m(1+4a2x2)x˙2+mgax2

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.

x¨=2gax

b.

m(1+4a2x2)x¨=2mgax+4ma2xx˙2

c.

x¨=2gax

d.

m(1+4a2x2)x¨=2mgax4ma2xx˙2

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 q is given by L=αq˙2+βq2 , where α and β are non –zero constants. If pq denotes the canonical momentum conjugate to q then which one of the following statements is CORRECT?

Choices

Choice (4) Response

a.

pq=2αq˙ and it is a conserved quantity

b.

pq=2αq˙ and it is not a conserved quantity

c.

pq=2βq and it is not a conserved quantity

d.

pq=2βq and it is a conserved quantity

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