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Problem 33 Hard Difficulty

A thin wire is bent into the shape of a semicircle $ x^2 + y^2 = 4 $, $ x \geqslant 0 $. If the linear density is a constant $ k $, find the mass and center of mass of the wire.

Answer

Mass of the wire is 2$\pi k$ Centre of mass of the wire is $$\left(\frac{4}{\pi}, 0\right)$$

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Video Transcript

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