### Problem:A thin rod of length \( L = 3.00 \, \text{m} \) with variable mass density \(\lambda(x) = 3.00x^2 \, \text{kg/m}\) lies on the x-axis with one end at the origin. Where on the x-axis is the **center of mass** of this rod? *(Note: this is a variable mass density)*### Options:- \(2.50 \, \text{m}\)- \(1.50 \, \text{m}\)- \(2.25 \, \text{m}\)- \(2.70 \, \text{m}\)- \(1.88 \, \text{m}\)### Explanation:This problem requires finding the center of mass of a rod with a given variable mass density. The mass density function \(\lambda(x) = 3.00x^2\) indicates that the mass distribution increases with the square of the distance from the origin. The center of mass will be calculated using the integral of the mass distribution across the length of the rod, considering symmetry and variable density.

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Answered: A thin rod of length L = 3.00m with…

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A thin rod of length L = 3.00m with variable mass density (x) = 3.00x² kg/m lies on the x-axis with one end at the origin. Where on the x-axis is the center of mass of this rod? {note this is a variable mass density}