**Computation**A thin rod of length \( L \) and mass \( m \) has a linear density \( \lambda(x) = Ax^2 \) where \( A \) is a constant and \( x \) is the distance from the rod's left end. Locate the rod’s center of mass (from \( x = 0 \)) in terms of its length by filling in the missing factor below.[Hint: In terms of \( A \) and \( L \), the rod’s mass is \( M = \int_0^L \lambda \, dx \). Evaluate that integral and substitute into the denominator of the center of mass definition: \[ x_{cm} = \frac{\int_0^M x \, dm}{\int_0^M \, dm} = \frac{\int_0^L x \lambda(x) \, dx}{M} \]The constant \( A \) will cancel and you’ll be left with an answer proportional to \( L \).]\[ x_{cm} = \, \_\_\_\_\_ \, L \]Record your numerical answer below, assuming three significant figures. Remember to include a “-" when necessary. [Blank space provided for answer]

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A thin rod of length L and mass m has a linear density X(x) = Ax² where A is a constant and is the distance from the rod's left end. Locate the rod's center of mass (from x = = 0) in terms of its length by filling in the missing factor below.

A thin rod of length L and mass m has a linear density X(x) = Ax² where A is a constant and is the distance from the rod's left end. Locate the rod's center of mass (from x = = 0) in terms of its length by filling in the missing factor below.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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