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A disc of radis R is cut out from a larg...

A disc of radis R is cut out from a larger disc of radius 2R in such a way that the edge of the hole touches the edge of the disc. Locate the centre of mass of the residual disc.

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Mass can be assumed to be uniformly distributed proportional to area. Area of original dise is four times to that of the hole.
Let us select centre of disc as origin and X-axis along its line of symmetry as shown in figure. We can assume negative mass for the hole. Given state of system can be described as mass 4M kept at (0,0) and M at (R,0). We know that centre of mass lies on X-axis and coordinate can be written as follows:
`x=(3Mxx0+(-M)xxR)/(4M-M)=(R)/(3)`
Hence centre of mass of the system lies at a distance R/3 towards left of its centre.
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