Locate the centre of mass of the arrangement | vedclass

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(C) Let the mass of each rod be $m$. The arrangement consists of three rods:$1$. Vertical rod along the $y$-axis from $y=0$ to $y=L$. Its centre of ma

Vedclass · Accepted Answer

$\left(\frac{L}{3}, \frac{L}{2}\right)$

Vedclass · Answer

(C) Let the mass of each rod be $m$. The arrangement consists of three rods:$1$. Vertical rod along the $y$-axis from $y=0$ to $y=L$. Its centre of mass is at $(0, L/2)$.$2$. Horizontal rod along the $x$-axis from $x=0$ to $x=L$. Its centre of mass is at $(L/2, 0)$.$3$. Horizontal rod at $y=L$ from $x=0$ to $x=L$. Its centre of mass is at $(L/2, L)$.The $x$-coordinate of the centre of mass is $X_{cm} = \frac{m(0) + m(L/2) + m(L/2)}{m + m + m} = \frac{mL}{3m} = \frac{L}{3}$.The $y$-coordinate of the centre of mass is $Y_{cm} = \frac{m(L/2) + m(0) + m(L)}{m + m + m} = \frac{m(3L/2)}{3m} = \frac{L}{2}$.Thus,the centre of mass is at $\left(\frac{L}{3}, \frac{L}{2}\right)$.

Locate the centre of mass of the arrangement shown in the figure. The three rods are identical in mass and length.

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