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Q.

A square shaped hole of side l=a2  is carved out at a distance  d=a2  from the centre ‘O’ of a uniform circular disk of radius a. If the distance of the centre of mass of the remaining portion from O is  −aX, value of X (to the nearest integer) is ______

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answer is 0023.00.

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Detailed Solution

CM of remaining portion shifts towards -x axisMremainingx=Mremovedd​⇒Mtotal−Mremovedx=Mremovedd​⇒x=Mremoved dMtotal−Mremoved=σl2dσπa2−σl2        Mremoved=σl2,Mtotal=σπa2​⇒x=l2dπa2−l2=a8π−2=a23.12
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