Classical Mechanics-Dynamical System (CSIR Physical Sciences): Questions 1 - 5 of 6

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Question number: 1

» Classical Mechanics » Dynamical System

Appeared in Year: 2011

MCQ▾

Question

A constant force F is applied to applied to a relativistic particle of rest mass m. If the particle starts from rest at t=0 , its speed after a time t is - (December)

Choices

Choice (4) Response

a.

Ftm

b.

c(IeFtmc)

c.

ctanh(Ftm)

d.

FctF2t2+m2c2

Question number: 2

» Classical Mechanics » Dynamical System

Appeared in Year: 2014

MCQ▾

Question

The radius of Earth is approximately 6400 km. The height h at which the acceleration due to Earth’s gravity differs from g at the Earth’s surface by approximately 1 % is – (December)

Choices

Choice (4) Response

a.

48 km

b.

16 km

c.

32 km

d.

64 km

Question number: 3

» Classical Mechanics » Dynamical System

Appeared in Year: 2011

MCQ▾

Question

A particle of unit mass moves in a potential V(x)=ax2+bx2 , where a and b are positive constants. The angular frequency of small oscillations about the minimum of the potential is – (June)

Choices

Choice (4) Response

a.

8a

b.

8ab

c.

8ba

d.

8b

Question number: 4

» 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: 5

» 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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