A circular disc of radius `R` is removed from a bigger circular disc of radius `2 R` such that the circumferences of the discs coincide. The center of mass of new disc is `alpha R` from the center of the bigger disc. The value of `alpha` is

Options

A. `1//3`
B. `1//2`
C. `1//6`
D. `1//4`

Answer

A

Explanation

Shift of centre of mass `x=(r^(2)a)/(R^(2)-r^(2))`
Where `r=` radius of removed disc
`R`=radius of original disc
`a`=distance between the centres
Note: in this question shift must be `propR` for exact approach to the solution