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*Question* :- Find the ```Centre of Mass``` of the ```system``` → From a solid sphere of radius r having uniform density , a small sphere of radius r/2 is cut at a distance of r/2 from the centre

*Question* :-
Find the ```Centre of Mass``` of the ```system``` →
From a solid sphere of radius r having uniform density , a small sphere of radius r/2 is cut at a distance of r/2 from the centre

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1 Answers

Khimraj
3007 Points
5 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/8.
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 = 7M/8.
From conservation of centre of mass : 
C.M. of remaining portion = C.M. of big sphere + C.M. of the small sphere.
=> \frac{7M}{8}*(-OP) = M*0 + \frac{M}{8}*\frac{R}{2}
=> OP = -\frac{R}{14}
So, the centre of mass of the remaining portion shifts to \frac{R}{14} from tge centre of the circle.
Hope it clears.

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