(1) A rod of length L has a small square cross section b²; the density of the material is p. Just by intuition you know that the center of mass of this rod is "in the middle", at L/2; i.e. this is where you would support the rod to balance it on your finger. a. Calculate the total mass of this rod; and calculate the mass of a tiny bit of the rod, of length AL and cross-section b². b. Show (i.e. prove) that the center of mass is at L/2 by starting with the definition of the center of mass position for a continuous object.

(1) A rod of length L has a small square cross section b²; the density of the material is p. Just by intuition you know that the center of mass of this rod is "in the middle", at L/2; i.e. this is where you would support the rod to balance it on your finger. a. Calculate the total mass of this rod; and calculate the mass of a tiny bit of the rod, of length AL and cross-section b². b. Show (i.e. prove) that the center of mass is at L/2 by starting with the definition of the center of mass position for a continuous object.

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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Helllo,

Can someone please solve this problem?

Thanks

**Problem (I): Rod with Uniform Density**

A rod of length \( L \) has a small square cross section \( b^2 \); the density of the material is \( \rho \). Intuitively, the center of mass of this rod is "in the middle", at \( L/2 \). This is the point where you would support the rod to balance it on your finger.

**Tasks:**
a. Calculate the total mass of this rod; and calculate the mass of a tiny bit of the rod, of length \( \Delta L \) and cross-section \( b^2 \).

b. Show (i.e., prove) that the center of mass is at \( L/2 \) by starting with the definition of the center of mass position for a continuous object.

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