Question Compute the center of mass on a rod of density p = 4 with 3 € (0,6). 2
706KOG The Asker · Calculus
Transcribed Image Text: Compute the center of mass on a rod of density p = 4 with 3 € (0,6). 2
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Solutiongiven density \rho=4 with x \in(0,6)\begin{aligned}\text { mass } & =\int_{0}^{6} \rho d x \\\text { mass } & =\int_{0}^{6} 4 d x=4[x]_{0}^{6}=4(6-0)=24 \\\text { moment } & =\int_{0}^{6} \rho x d x \\\text { moment } & =\int_{0}^{6} 4 x d x=4\left[\frac{x^{2}}{x}\right]_{0}^{6}=2[36-0]=72\end{aligned}centre of mass\bar{x}=\frac{\text { mowent }}{\text { mass }}=\frac{72}{24}=3 \text { Ans } ...