A lamina is made by removing a small disc of diameter 2 R from a bigger disc of uniform mass density and radius 2R, as shown in figure. A second similar disc is made but instead of hole a disc of triple the density as of first it filled in the hole. Centre of mass is calculated in both the cases and was found at a distance `r_(1) & r_(2)` from centre `O` respectively find the ratio `|(2r_(2))/(r_(1))|`

Answer

2

Explanation

`r_(1)=([-sigmaxxpiR^(2)]xxR)/([-sigmaxxpiR^(2)]+[sigmaxxpi(2R)^(2)])`
`&r_(2)=([2sigmaxxpiR^(2)]xxR)/([2sigmaxxpiR^(2)]+[sigmaxxpi(2R)^(2)])implies|(2r_(2))/(r_(1))|=2`