Four identical spheres, each of radius 10 ,cm | vedclass

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(C) The given situation is shown in the figure where $A, B, C, D$ are the centers of the four spheres forming a square of side $a = 20 \,cm$.Since all

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$10 \sqrt{2} \,cm$

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(C) The given situation is shown in the figure where $A, B, C, D$ are the centers of the four spheres forming a square of side $a = 20 \,cm$.Since all four spheres are identical and have equal masses, the center of mass of the system will coincide with the geometric center of the square formed by their centers, denoted by point $O$.The distance of the center of mass from the center of any sphere (e.g., center $A$) is the distance $AO$.In a square of side $a = 20 \,cm$, the length of the diagonal $AC$ is given by $AC = \sqrt{a^2 + a^2} = a\sqrt{2} = 20\sqrt{2} \,cm$.The distance from the center of the square to any vertex is half the length of the diagonal:$AO = \frac{AC}{2} = \frac{20\sqrt{2}}{2} = 10\sqrt{2} \,cm$.

Four identical spheres, each of radius $10 \,cm$ and equal mass $1 \,kg$, are placed on a horizontal surface touching each other such that their centers are located at the vertices of a square of side $20 \,cm$. What is the distance of their center of mass from the center of any sphere?

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