Figure shows the circular disc of diameter 56 cm after a circular portion of diameter 42 cm is removed.
We know that point O is centre of mass for the full disc before removing the above mentioned circular portion.
we take the point O as reference to calculate the centre of mass by considering the full disc is made of two objects, i.e., the disc showed as coloured one(white colour circular portion is removed) and the removed white colour circular portion. Let point Q which is centre of mass of coloured object, be at a distance x cm from point O.
(m1 × x + m2 × 7 )/(m1+m2) = 0 ..........................(1)
where m1 and m2 are masses of coloured object and white circular disc respectively.
We have written 0 in right hand side of eqn.(1) because we took point O which is centre of mass of full circular disc as reference point
from eqn.(1) we get x = - (m2×7)/m1...............(2)
mass of circular objects are proportional to square of diameter because thickness and density are same.
hence we write eqn.(2) as , x = -(42×42×7) / [ (56×56)-(42×42)] = -9 cm