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Question

A circular hole of radius r is made in a disk of radius R and of uniform thickness at a distance a from the centre of the disk. The distance of the new centre of mass from the original centre of mass is :

40044_6a91dffcb4c040a48b8ee2d9b467a99a.png

A
aR2R2r2
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B
ar2R2r2
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C
a(R2r2)r2
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D
a(R2r2)R2
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Solution

The correct option is B ar2R2r2
Suppose the new center of mass is at a distance Xrem from the center of bigger disc and the center of mass of the
hole will be at a distance Xrmd=a from the center of the bigger disk.

Now area of bigger disk is πR2 and that of hole is πa2

denoting the area of removed part as Armd=πr2

and the area of remaining part as Arem=π(R2r2)

and using the formula XremArem=XrmdArmd

we get Xrem=ar2R2r2

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