Classical Mechanics (GATE Physics): Questions 24 - 27 of 38

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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, V(x)=x(x2)2 . The particle is found to be in stable equilibrium at the point x=2 . The time period of oscillation of the particle is –

Choices

Choice (4) Response

a.

π

b.

π2

c.

3π2

d.

2π

Question number: 25

» Classical Mechanics » Relativistic Kinematics

Appeared in Year: 2012

MCQ▾

Question

A rod of proper length L0 oriented parallel to the X- axis moves with speed 2C3 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 C2 with respect to the S – frame. The length of the rod as measured by the observer is

Choices

Choice (4) Response

a.

0.48L0

b.

0.87L0

c.

0.35L0

d.

0.97L0

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: 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.

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: 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.

x¨=2gax

b.

m(1+4a2x2)x¨=2mgax+4ma2xx˙2

c.

x¨=2gax

d.

m(1+4a2x2)x¨=2mgax4ma2xx˙2

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