A uniform rod of length L and mass M is place | vedclass

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(B) For a uniform rod of length $L$ and mass $M$ placed along the $x$-axis with one end at the origin $(0, 0)$,the linear mass density $\lambda$ is co

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$(L/2, 0)$

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(B) For a uniform rod of length $L$ and mass $M$ placed along the $x$-axis with one end at the origin $(0, 0)$,the linear mass density $\lambda$ is constant,given by $\lambda = M/L$.The $x$-coordinate of the centre of mass is calculated as:$X_{cm} = \frac{1}{M} \int x \, dm$Since $dm = \lambda \, dx = (M/L) \, dx$,we have:$X_{cm} = \frac{1}{M} \int_{0}^{L} x \cdot \frac{M}{L} \, dx$$X_{cm} = \frac{1}{L} \int_{0}^{L} x \, dx = \frac{1}{L} \left[ \frac{x^2}{2} \right]_{0}^{L} = \frac{1}{L} \cdot \frac{L^2}{2} = L/2$.Since the rod lies on the $x$-axis,the $y$-coordinate of the centre of mass is $0$.Therefore,the centre of mass is at $(L/2, 0)$.

$A$ uniform rod of length $L$ and mass $M$ is placed along the $x$-axis with its one end at the origin. The centre of mass of the rod is located at:

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