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Question no-1

Asked by shobhit | 08 May, 2018, 08:31: AM
First Let us calculate the centre of mass of sector of circular disk. As shown in figure the sector is divided into strips of width dr and let us assume one such strip at a distance r from point O. Let ρ be the density per unit area. The mass dm of the strip is given by
Let RCMS be the location of centre of mass of sector of circular disk that has mass MS. Then RCMS can be determined as given below
where RS is radius of sector. Mass of sector is given by
substituting for mass of sector using (3) in (2) and after simplification we get RCMS = (2/3)RS.
Centre of mass of the combined system as shown in above figure  is given by

MS×RCMS + MR×RCMR = 0 [ Since we want Centre of mass of combined system at Origin O ]
since mass of both objects are same, we have
RCMS + RCMR =0;  or  RCMR = -RCMS = (2/3)×RS = (2/3)×12 = 8 cm

Answered by Thiyagarajan K | 08 May, 2018, 04:31: PM

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