Answer :

a) Let M be the mass of half disc and R be its radius.

Mass per unit length

Let cut a semi-circular ring out of this semi disc at distance r and r+dr from centre.

So, Area of element

Mass of elementary ring

For this semi-circular ring centre of mass is

So,

Hence centre of mass of semi-circular disc

b) Let M be the mass of quarter disc and R be its radius.

Mass per unit length

Similarly, as above part

Area of element

Mass of elementary ring

For this semi-circular ring centre of mass is

So,

Hence centre of mass of Quarter disc

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