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in Physics by (50.2k points)

From a uniform circular disc of diameter d, a circular disc of diameter d/6 and having centre at a distance d/4 from the centre of the disc is scooped out. Determine the centre of mass of the remaining portion.

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Suppose mass per unit are a of the disc = m

Mass of the disc, M = π (d/2)2 m = πmd2/4

Mass of portion removed,

 M' = π(d/12)2 m = πmd2/144

Let centre O of the disc be taken as the origin. Suppose masses M and M' are concentrated at O and O' respectively. Fig,

As the portion is removed, taking M' as negative, CM of the remaining portion is at a distance 'x' from 'O' where

Negative sign indicates CM is to the left of origin O.

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