Classical Mechanics (CSIR Physical Sciences): Questions 35 - 38 of 59

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Question number: 35

» Classical Mechanics » Conservation Laws and Cyclic Coordinates

Appeared in Year: 2012

MCQ▾

Question

A planet of mass m moves in the gravitational field of the Sun (mass M). If the semi – major and semi – minor axes of the orbit are a and b respectively, the angular momentum of the planet is – (December)

Choices

Choice (4) Response

a.

2GMm2(a+b)

b.

2GMm2(ab)

c.

2GMm2aba+b

d.

2GMm2abab

Question number: 36

» Classical Mechanics » Dynamical System

Appeared in Year: 2014

MCQ▾

Question

A canonical transformation relates the old coordinates (q,p) to the new ones (Q,P) by the relations Q=q2 and P=p2q . The corresponding time – independent generating function is – (June – 2014)

Choices

Choice (4) Response

a.

Pq2

b.

q2P

c.

q2P

d.

qP2

Question number: 37

» Classical Mechanics » Conservation Laws and Cyclic Coordinates

Appeared in Year: 2013

MCQ▾

Question

A particle of mass m is at the stable equilibrium position of its potential energy, V(x)=axbx3 ; where a,b are positive constants. The minimum velocity that has to be imparted to the particle to render its motion unstable is – (June)

Choices

Choice (4) Response

a.

(16a327m2b)14

b.

(3a364m2b)14

c.

(64a327m2b)14

d.

(64a39m2b)14

Question number: 38

» Classical Mechanics » Dynamical System

Appeared in Year: 2014

MCQ▾

Question

The time evolution of one – dimensional system is described by dxdt=(x+1)(x2b2) . If this has one stable and two unstable fixed points, then the parameter b satisfies – (June – 2014)

Choices

Choice (4) Response

a.

0<b<1

b.

b>1

c.

b<1

d.

b=2

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