(A) The original square plate is symmetric about both the $X$ and $Y$ axes,meaning its center of mass is at the origin $O(0, 0)$.When four identical s

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(A) The original square plate is symmetric about both the $X$ and $Y$ axes,meaning its center of mass is at the origin $O(0, 0)$.When four identical small squares are removed from the four corners,the remaining shape retains symmetry about both the $X$ and $Y$ axes.Since the mass distribution remains symmetric with respect to both axes,the center of mass of the remaining system will still coincide with the geometric center of the original square.Therefore,the center of mass remains at the origin $O$.

Class 11 Physics System of Particles and Rotational Motion Centre of Mass of Composite Bodies and Cavity Problen of Centre of mass

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$A$ uniform square plate is shown in the figure. Four identical small squares are removed from its corners. Where will the $C.M.$ (Center of Mass) be located after removing all four squares? Give the answer in terms of quadrants and axes.

A
At point $O$
B
In the $III$ quadrant
C
On the $OY'$ axis
D
In the $IV$ quadrant

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Class 11 Questions

Class 11

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System of Particles and Rotational Motion

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Centre of Mass of Composite Bodies and Cavity Problen of Centre of mass

$A$ uniform square plate of side $a$ has a circular hole of diameter $a$ cut out from it as shown in the figure. The center of the hole is at $(a/4, a/4)$ from the center of the square. The distance of the center of mass of the resulting plate from the center of the square is:

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The figure shows a composite system of two uniform rods of lengths as indicated. The coordinates of the centre of mass of the system of rods are ...........

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$A$ uniform square plate of side $a$ is placed in the $xy$-plane with its center at the origin. If a circular portion of diameter $a$ is removed from the plate as shown in the figure,what is the position of the center of mass of the remaining portion?

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$A$ uniform circular disc has radius $r$. $A$ square portion of diagonal $r$ is cut from it. The centre of mass of the remaining disc from the centre of the disc is

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$A$ uniform square plate of side $a$ has a hole of side $b$ cut out of it as shown in the figure. The hole is centered at $(a/4, a/4)$ from the center of the square plate. The distance of the center of mass of the remaining part from the center of the square plate is:

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$A$ uniform square plate is shown in the figure. Four identical small squares are removed from its corners. Where will the $C.M.$ (Center of Mass) be located after removing all four squares? Give the answer in terms of quadrants and axes.

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$A$ uniform square plate of side $a$ has a circular hole of diameter $a$ cut out from it as shown in the figure. The center of the hole is at $(a/4, a/4)$ from the center of the square. The distance of the center of mass of the resulting plate from the center of the square is:

The figure shows a composite system of two uniform rods of lengths as indicated. The coordinates of the centre of mass of the system of rods are ...........

$A$ uniform square plate of side $a$ is placed in the $xy$-plane with its center at the origin. If a circular portion of diameter $a$ is removed from the plate as shown in the figure,what is the position of the center of mass of the remaining portion?

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$A$ uniform square plate of side $a$ has a hole of side $b$ cut out of it as shown in the figure. The hole is centered at $(a/4, a/4)$ from the center of the square plate. The distance of the center of mass of the remaining part from the center of the square plate is:

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