A disc of radis R is cut out from a larger disc of radius 2R in such a way that the edge of the hole touches the edge of the disc. Locate the centre of mass of the residual disc.

Explanation

Let 0 be the origin of the system
R=radius of the smalle rdisc
2R=radius of the biger disc thesmaller disc is cut out from the bigger disc.
From the ure

`m_1=piR^2Trho,x_1=R,y_1=0`
`m_2=pi(2R)^2Trho,x_2=0, y_2=0`
`:.`position of C.M.
`=((piR^2TrhoR+0m_2)/(-piR^2Trho+pi(2R)^2Trho, (0+0)/(m_1+m_2))`
`=((-pir^2TrhoR)/(3piR^2Trho),0)=R/3`
C.M. is at `R/3` from th centre of bigger disc away from centre of the hole.