A motion is described by the linear (in a) functionp(a, t) = F(t)awith det F(t) =1+tfor all times. The mass density at time t = 0 is given by po(@) = 1+ |a. Choose the correct expression for the Lagrangian mass density Pm(a,t) andthe Eulerian mass density p(x,t) at any subsequent time.Pm(a, t) = (1+t)(1+|a|) and p(x, t) = (1+t)(1+|F-'(t)x|)Pm(a, t)1+|F(t)a|1+tand ρ(π, )1+|æ|1+tPm(a, t) = (1+t)(1+|F(t)a|) and p(x, t) = (1+t)(1+ |x|)Pm(a, t)1+|a|IHt and p(x, t)1+|F_'(t)x|1+t

In field theories, a Lagrangian Density is utilised. Lagrangian density throughout space. In…

A motion is described by the linear (in a) function p(a,t) = F(t)a with det F(t) = 1+t for all times. The mass density at time t = 0 is given by po(a) = 1+ |a|.Choose the correct expression for the Lagrangian mass density pPm (a, t) a the Eulerian mass density p(x, t) at any subsequent time. Pm(a, t) = (1+t)(1+ |a|) and p(æ, t) = (1+ t)(1 + |F-'(t)x|) O Pm (a, t) = 1+ROal and p(x, t) = 1+|F(t)a| Pm(a, t) = (1+t)(1+|F(t)a|) and p(x, t) = (1 + t)(1+|æ|) 1+|a| Pm(a, t) = a and p(x, t) = !+F'(t)x| OO O O

A motion is described by the linear (in a) function p(a,t) = F(t)a with det F(t) = 1+t for all times. The mass density at time t = 0 is given by po(a) = 1+ |a|.Choose the correct expression for the Lagrangian mass density pPm (a, t) a the Eulerian mass density p(x, t) at any subsequent time. Pm(a, t) = (1+t)(1+ |a|) and p(æ, t) = (1+ t)(1 + |F-'(t)x|) O Pm (a, t) = 1+ROal and p(x, t) = 1+|F(t)a| Pm(a, t) = (1+t)(1+|F(t)a|) and p(x, t) = (1 + t)(1+|æ|) 1+|a| Pm(a, t) = a and p(x, t) = !+F'(t)x| OO O O

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

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A motion is described by the linear (in a) function
p(a, t) = F(t)a
with det F(t) =1+tfor all times. The mass density at time t = 0 is given by po(@) = 1+ |a. Choose the correct expression for the Lagrangian mass density Pm(a,t) and
the Eulerian mass density p(x,t) at any subsequent time.
Pm(a, t) = (1+t)(1+|a|) and p(x, t) = (1+t)(1+|F-'(t)x|)
Pm(a, t)
1+|F(t)a|
1+t
and ρ(π, )
1+|æ|
1+t
Pm(a, t) = (1+t)(1+|F(t)a|) and p(x, t) = (1+t)(1+ |x|)
Pm(a, t)
1+|a|
IHt and p(x, t)
1+|F_'(t)x|
1+t

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