Classical Mechanics (GATE Physics): Questions 24 - 27 of 79

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Question number: 24

» Classical Mechanics » Small Oscillations and Normal Modes

Appeared in Year: 2012

MCQ▾

Question

A particle of unit mass moves along the X – axis under the influence of a potential, Equation . The particle is found to be in stable equilibrium at the point Equation . The time period of oscillation of the particle is –

Choices

Choice (4) Response

a.

Equation

b.

Equation

c.

Equation

d.

Equation

Question number: 25

» Classical Mechanics » Relativistic Kinematics

Appeared in Year: 2012

MCQ▾

Question

A rod of proper length Equation oriented parallel to the X- axis moves with speed Equation along the Y – axis in the S – frame, where C is the speed of light in free space. The observer is also moving along the X – axis with speed Equation with respect to the S – frame. The length of the rod as measured by the observer is

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: 26 (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: 27 (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

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