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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