A uniform square plate abcd has a mass of 1 , | vedclass

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(C) Let the side length of the square plate be $L$. The center of the square $O$ is at the origin $(0,0)$.The coordinates of the corners are: $a(-L/2,

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$OY$

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(C) Let the side length of the square plate be $L$. The center of the square $O$ is at the origin $(0,0)$.The coordinates of the corners are: $a(-L/2, L/2)$,$b(L/2, L/2)$,$c(L/2, -L/2)$,and $d(-L/2, -L/2)$.The mass of the plate $M = 1 \, kg = 1000 \, g$ is concentrated at the center $O(0,0)$.Two point masses $m = 20 \, g$ are placed at $b(L/2, L/2)$ and $c(L/2, -L/2)$.The new $x$-coordinate of the center of mass is $X_{cm} = \frac{M(0) + m(L/2) + m(L/2)}{M + 2m} = \frac{mL}{M + 2m}$.The new $y$-coordinate of the center of mass is $Y_{cm} = \frac{M(0) + m(L/2) + m(-L/2)}{M + 2m} = 0$.Since $Y_{cm} = 0$ and $X_{cm} > 0$,the center of mass shifts along the positive $x$-axis,which corresponds to the line $OY$.

$A$ uniform square plate $abcd$ has a mass of $1 \, kg$. If two point masses,each of $20 \, g$,are placed at the corners $b$ and $c$ as shown,then the centre of mass shifts on the line

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