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Question

Figure shows a uniform disc of radius R, from which a hole of radius R2 has been cut out from left of the center and is placed on right of the center of disc. Find the centre of mass of the resulting disc.


A

(R4,0)

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B

(R4,0)

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C

(R6,0)

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D

(R6,0)

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Solution

The correct option is A

(R4,0)


Mass of the cut out disc
m=MπR2×π(R2)2=M4
let center of the disc be at the origin of coordinates, then we can write the C.M. of the system as;
xcm=MRmr+mrMm+m=MOM4(R2)+M4(R2)MM4+M4=R4 and ycm=0


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