CSIR Physical Sciences: Questions 388 - 390 of 401

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Passage

In the absence of an applied torque a rigid body with three distances principal moments of inertia given by I1,I2andI3 is rotating freely about a fixed point inside the body. The Euler equations for the components of its angular velocity (ω1,ω2,ω3) are

ω˙1=I2I1I1ω2ω3,ω˙2=(I3I1)I2ω1ω3,ω˙3=I1I2I3ω1ω2 (June)

Question number: 388 (2 of 2 Based on Passage) Show Passage

» Classical Mechanics » Rigid Body Dynamics - Moment of Inertia Tensor

Appeared in Year: 2011

MCQ▾

Question

The constant of motion are –

Choices

Choice (4) Response

a.

I1ω12+I2ω22+I3ω32andω1+ω2+ω3

b.

I1ω12+I2ω22+I3ω32andI12ω12+I22ω22+I32ω32

c.

ω12+ω22+ω32andI1ω1+I2ω2+I3ω3

d.

ω12+ω22+ω32andI12ω12+I22ω22+I32ω32

Passage

Consider the matrix M=(111111111) (June)

Question number: 389 (1 of 1 Based on Passage) Show Passage

» Mathematical Methods of Physics » Taylor & Laurent Series

Appeared in Year: 2011

MCQ▾

Question

The exponential of M simplifies to (I is the 3×3 identity matrix)

Choices

Choice (4) Response

a.

eM=I+33M

b.

eM=I+M+M22!

c.

eM=I+(e313)M

d.

eM=(e1)M

Question number: 390

» Classical Mechanics » Special Theory of Relativity » Lorentz Transformations

Appeared in Year: 2016

MCQ▾

Question

Let (x,t) and (x,t) be the coordinate systems used by the observers O and O , respectively. Observer O moves with a velocity v=βc along their common positive x axis. If x+=x+ct and x=xct are the linear combinations of the coordinates the Lorentz transformation relating O and O takes the form – (June)

Choices

Choice (4) Response

a.

x+=1+β1βx+andx=1β1+βx

b.

x+=1β1+βx+andx=1+β1βx

c.

x+=xβx+1β2andx=x+βx1β2

d.

x+=x+βx1β2andx=xβx+1β2

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