Figure shows a uniform disc of radius `R`, from which a hole of radius `R/2` has been cut out from left of the centre and is placed on the right of the centre of the disc. Find the CM of the resulting disc.
Text Solution
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Mass of the cut out disc is `m=M/(piR^(2))xxpi(R/2)^(2)=M/4` Let centre of the disc is at origin of the coordinates. Then we can write the CM of the system as `x_(CM)=(vec(MR)-vec(mr)+vec(mr))/(M+m+m)=(Mxx0-M/4((-R)/2)+M/4(R/2))/(M-M/4+M/4)=R/4` `y_(CM)=0`
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