A sphere of diameter r is cut from a sphere of radius r such that the center of mass of the remaining mass be at maximum distance from original center then the distance is?

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A sphere of diameter r is cut from a sphere of radius r such that the center of mass of the remaining mass be at maximum distance from original center then the distance is?

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A sphere of diameter r is cut from a sphere of radius r such that the ...

Let x = distance between COM from the original center of the sphere, after the small sphere is cut off from it.

Let the density of the sphere be = d

Mass of big sphere (full) = 4/3 * π r� * d

Mass of the small sphere cut off from it = 4/3 * π (r/2)^3 * d

Mass of the remaining object = 7/6 π r^3 * d

Position of the COM of the complete sphere = 0

=> - x * 7/6 π r^3 d + r/2 * 4/3 π (r/2)^3 * d = 0

=> x = r / 14

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