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The linear mass density lambda of a rod ...

The linear mass density lambda of a rod AB is given by `lambda =alpha+betax` kg/m taking O as origin. Find the location of the centre of mass from the end A?

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To find the location of the center of mass of a rod AB with a linear mass density given by \(\lambda = \alpha + \beta x\) kg/m, we will follow these steps: ### Step 1: Understand the Problem We have a rod of length \(L\) placed along the x-axis. The linear mass density \(\lambda\) varies with position \(x\). We need to find the x-coordinate of the center of mass from the end A (which we can consider as \(x = 0\)). ### Step 2: Define the Differential Mass Element The differential mass element \(dm\) can be expressed in terms of the linear mass density: \[ ...
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