Q.

A disc of radius r is removed from the disc of radius R then which of the following are true

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a

Center of mass must lie where mass exists

b

The minimum shift in center of mass cannot be greater than  r2R+r

c

The shift in center of mass is r2R+r

d

The minimum shift in center of mass is zero

answer is A, B.

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Detailed Solution

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Shift in the centre mass will be minimum, when the cut is concentric.

Maximum shift will be when it is adjacent to the edge 

 xcm=m1r1+m2r2m1+m2

=λπR2(0)-λπr2(R-r)λπR2-λπr2=r2R+r

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