Let mass per unit area of the disc
=m Total mass of disc,
M=Ï€R2m Mass of the scooped out portion of the disc,
M′=πr2m For small objects, centre of gravity and centre of mass are at same position.
We take the centre
O of the disc as the origin. The masses
M and
M′ can be supposed to be concentrated at the centres of the disc and scooped out portion respectively. The mass
M′ of the removed portion is taken negative.
The
x -coordinate of the centre of mass of the remaining portion of the disc will be
⇒xCM=−lcm Hence, distance of centre of gravity of the resulting flat body from the centre of the original disc will be
1cm left side.