GATE Physics: Questions 105 - 108 of 290

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Question number: 105

» Classical Mechanics » Conservation Laws

Appeared in Year: 2015

MCQ▾

Question

A particle with rest mass M is at rest and decays into two particles of equal rest masses 310M , which move along the Z – axis. Their velocities are given by,

Choices

Choice (4) Response

a.

v1=v2=(0.8c)z^

b.

v1=v2=(0.6c)z^

c.

v1=v2=(0.8c)z^

d.

v1=(0.6c)z^;v2=(0.8c)z^

Question number: 106

» Atomic and Molecular Physics » Raman Effect

Appeared in Year: 2012

MCQ▾

Question

The first Stokes line of rotational Raman spectrum is observed at 12.96cm1 . Considering the rigid rotor approximation, the rotational constant is given by –

Choices

Choice (4) Response

a.

1.62cm1

b.

3.24cm1

c.

6.48cm1

d.

2.16cm1

Question number: 107

» Mathematical Physics » Matrices

Appeared in Year: 2012

MCQ▾

Question

The eigen values of the matrix (010101010) are –

Choices

Choice (4) Response

a.

0,2,2

b.

12,12,0

c.

0,1,1

d.

2,2,0

Question number: 108

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

Appeared in Year: 2012

MCQ▾

Question

A particle of mass m is attached to a fixed point O by a weightless inextensible string of length a . It is rotating under the gravity as shown in the figure.

Ellipse c Ellipse c: Ellipse with foci C, D passing through EArc d Arc d: CircularArc [P, Q, R] Segment f Segment f: Segment [F, G] Segment g Segment g: Segment [H, I] Vector u Vector u: Vector [A, B] Vector u Vector u: Vector [A, B] Vector v Vector v: Vector [J, K] Vector v Vector v: Vector [J, K] Vector w Vector w: Vector [L, M] Vector w Vector w: Vector [L, M] Vector a Vector a: Vector [N, O] Vector a Vector a: Vector [N, O] Vector a Vector a: Vector [N, O] Point G Point G: Point on uPoint G Point G: Point on uPoint J Point J: Point on cPoint J Point J: Point on cPoint Q Q = (5.8, 3.7) Point Q Q = (5.8, 3.7) Point R R = (5.52, 2.42) Point R R = (5.52, 2.42) ? text1 = “? “Z text1_1 = “Z”a text1_2 = “a”m text1_3 = “m”g text1_4 = “g”O text1_5 = “O”

a Particle Rotates About Z – Axis

In figure a particle of mass m, is attached to a fixed point O by a weightless inextensible string. And this particle rotating about Z – axis.

The Lagrangian of the particle is,

L(θ,ϕ)=12ma2(θ˙2+sin2θϕ˙2)mgacosθ

Where, θ and ϕ are the polar angles.

The Hamiltonian of the particle is,

Choices

Choice (4) Response

a.

H=12ma2(pθ2+pϕ2sin2θ)mgacosθ

b.

H=12ma2(pθ2+pϕ2)+mgacosθ

c.

H=12ma2(pθ2+pϕ2)mgacosθ

d.

H=12ma2(pθ2+pϕ2sin2θ)+mgacosθ

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