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A small sphere of radius R is held against the inner surface of a larger sphere of radius 6R.The masses of large and small spheres are 4M and M respec.This arrangement is placed on a horizontal table.There is no friction bet any surfaces of contact.The small sphere is now released.Find the coordinates of the centre of the larger sphere when the smaller sphere reaches the other extreme position.

Asked by m.nilu 21st September 2018, 6:13 PM
Answered by Expert
Answer:
This is solved by Centre of Mass (COM) concept. There is no external force on the system of small and big sphere in horizontal direction.
So the COM remains at same position.
 
X-coordinate of COM begin mathsize 12px style equals space fraction numerator negative 5 R cross times M space plus space 0 cross times 4 M over denominator M plus 4 M end fraction space equals space minus R end style
Thus the COM is at a distance R away from the centre of big sphere. When the small sphere goes to the other extreme,
the COM remains at same position.  COM will be still at a distance R from centre of big sphere, but on the other side as shown in figure
Answered by Expert 27th September 2018, 3:52 PM
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