Mathematical Methods of Physics (CSIR Physical Sciences): Questions 63 - 65 of 65

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Passage

A resistance is measured by passing current through it and measuring the resulting voltage drop. If the voltmeter and the ammeter have uncertainties of 3% and 4% , respectively, then – (June)

Question number: 63 (2 of 2 Based on Passage) Show Passage

» Mathematical Methods of Physics » Dimensional Analysis

Appeared in Year: 2011

MCQ▾

Question

The uncertainty in the value of resistance is:

Choices

Choice (4) Response

a.

5.0%

b.

12.0%

c.

3.5%

d.

7.0%

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: 64 (1 of 1 Based on Passage) Show Passage

» Mathematical Methods of Physics » Eigenvalues and Eigenvectors

Appeared in Year: 2011

MCQ▾

Question

The equilibrium points in (ω1,ω2,ω3) space are –

Choices

Choice (4) Response

a.

(1,1, 0),(1, 0,1)and(0,1, 1)

b.

(1, 1,0),(1, 0,1)and(0, 1,1)

c.

(1, 0,0),(0, 1,0)and(0, 0,1)

d.

(1, 1,1),(1,1,1)and(0, 0,0)

Passage

Consider the matrix M=(111111111) (June)

Question number: 65 (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

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