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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.

Shaswata Biswas
132 Points
4 years ago
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.
=> $\dpi{120} \frac{3M}{4}*(-OP) = M*OO + \frac{M}{4}*\frac{R}{2}$
=> OP = $\dpi{120} -\frac{R}{6}$
So, the centre of mass of the remaining portion shifts to $\dpi{120} \frac{R}{6}$ from tge centre of the circle.
THANKS