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

Mass of disc `prop area`
`m_(1) prop pi( 2R)^(2) , m_(2) prop pi R^(2)`
`m_(1) = 4m , m_(2) = m`
`c.m.` of the remaining disc
`x_(c.m.) = (m_(1) x_(1) - m_(2) x_(2))/(m_(1) - m_(2)) = ( 4m xx 0 - m xx R)/( 4m - m) = -(R )/(3)`
`c.m.` of the remaining disc will be at distance `R//3 , left of O`.