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From a solid sphere of radius R a solid spherical mass of radius R/2 is cut out from near its surface. Find the shift in the position of C.O.M.
Let the mass of bigger sphere be M with rafius R. Then the mass of smaller sphere with radius R/2 is M/4.Let the centre of the big sphere which is its centre of mass be the origin O. Then the centre of mass of the small sphere is at a distance R/2 from O.When the small sphere is cut out, let the C.M. of the remaining portion shifts to P. Mass of remaining portion = 3M/4.From conservation of centre of mass : C.M. of remaining portion = C.M. of big sphere + C.M. of the small sphere.=> => OP = So, the centre of mass of the remaining portion shifts to from tge centre of the circle.THANKS
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