Classical Mechanics (CSIR Physical Sciences): Questions 50 - 52 of 59

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Question number: 50

» Classical Mechanics » Symmetry

MCQ▾

Question

The character table of C3V , the group of symmetries of an equilateral triangle is given below,

Table for character of C3v

In above table character table of C3v, the group of symmetries of an equilateral triangle is given.

χ(0)

χ(1)

χ(2)

1C1

1

1

b

3C2

1

a

c

2C3

1

1

d

In the above C1,C2,C3 denotes the three classes of C3V , containing 1, 3 and 2 elements respectively, and χ(0),χ(1)andχ(2) are the characters of the three irreducible representations Γ(0),Γ(1) and Γ(2) of C3V . The entries a,b,c and d in this table are, respectively –

Choices

Choice (4) Response

a.

2, 1,1, 0

b.

1, 1,1,1

c.

1, 2,0,1

d.

1, 1,0,1

Question number: 51

» Classical Mechanics » Special Theory of Relativity » Relativistic Kinematics

Appeared in Year: 2011

MCQ▾

Question

Two gravitating bodies A and B with masses mA and mB , respectively, are moving I circular orbit. Assume that mBmA and let the radius of the orbit of body A be RA . If the body A is losing mass adiabatically, its orbital radius RA is proportional to –

(June)

Choices

Choice (4) Response

a.

1mA

b.

1mA2

c.

mA2

d.

mA

Question number: 52

» Classical Mechanics » Lagrangian and Hamiltonian Formalism and Equations of Motion

Appeared in Year: 2011

MCQ▾

Question

The Hamiltonian of a particle of unit mass moving in the XY – plane is given to be:

H=xPxyPy12x2+12y2 in suitable units. The initial values are given to be (x(0),y(0))=(1, 1) and (Px(0),Py(0))=(12,12) . During the motion, the curves traced out by the particles in the xy – plane and the PxPy plane are (June)

Choices

Choice (4) Response

a.

both hyperbolas

b.

both straight lines

c.

a hyperbola and an ellipse, respectively

d.

a straight line and a hyperbola respectively

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