Question

A uniform disc of radius R is put over another unifrom disc of radius 2R of the same thickness and density. The peripheries of the two discs touch each other. Locate the centre of mass of the system.

Answer 1

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.