A circular plate of uniform thickness has a diameter of 28 cm. A circular portion of diameter 21 cm is removed from the plate as shown . O is the center of mass of complete plate. The position of center of mass of remaining portion will shift towards left from O by (in cm)

C1 is the center of mass of cut portion and C2 that of remaining portion. We have to find x2.x1=14−10.5=3.5cmMass will be proportional to area. So mass of the whole disc is M=kπ142Mass of cut portion m1=kπ(10.5)2Mass of the remaining portion m2=M−m1=kπ142−10.52=kπ(24.5) ×(3.5) Now, m1x1=m2x2⇒ x2=m1x1m2=kπ(10.5)2×3.5kπ(24.5)×3.5=4.5cm