From a uniform disc of radius R, a circular disc of radius R/2 is cut out. The centre of the hole is at R/2 from the centre of original disc. Locate the centre of gravity of the resultant flat body.

Explanation

Let the centre of the bigge disc be the origin.
`2R=Radius of bigger disc
R= Radius of smaller disc `
`m_1=muRxTxxrho`
`m_2=mu(2R)^2xxTxxrho`

`where T=Thickness of the two discs
`rho=Density of the two discs`
`:.` Position of the centre of mass
`((m_1x_1+m_2x_2)/(m_1+m_2),(m_1y_1+m_2y_2)/(m_1+m_2))`
`x_1=R,y_1=0`
`x_2=0, y_2=0`
`((piR^2TrhoR+0)/(muR^2TrhoR+mu(2R)^2Trho),0/(m_1+m_2))`
`((piR^2TrhoR)/(5muR^2Trho))=(R/4,0)`
At `R/5` from the centre of bigger disc towards.