A circular plate of uniform thickness has a diameter fo 56cm. A circular portion of diameter 42 cm is removed from one edge of the plate as shown in figure. Find the position of the centre of mass of the remaining portion.

Explanation

Here, radius of circular plate
`= (56)/(2)cm = 28 cm` with centre `O`. And radius of circular portion removed `= (42)/(2) = 21 cm` with centre `O_(1)`, Fig.
If `m` is mass per unit area of disc, then
`M = pi(28)^(2)m and m_(1) = pi (21)^(2)m`
Mass of shaded portion,
`m_(2) = M - m_(1) = [pi (28)^(2) - pi(21)^(2)]m`
`= 343 pi m`
If `m_(1)` and `m_(2)` are assumed to be concentrated at `O_(1)` and `O_(2)` respectively, and `O` is their centre of mass, then
moment of `m_(2)` about `O =` moment of `m_(1)` about `O`.
`m_(2) xx O_(2)O = m_(1) xx O_(1)O`
`O_(2)O = (m_(1))/(m_(2)) xx O_(1)O = (441pim)/(343pi m) xx 7 cm`
`= 9cm`
This is the distance of c.m. of remaining portion of disc from of disc.