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

Options

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

Answer

B

Explanation

In Fig. `O` is the centre of circular disc of radius `2R` and mass `M.C_(1)` is centre of disc of radius `R`, which is removed. If `rho` is mass per unit area of disc, then `M = pi(2R)^(2)rho`
Mass of disc removed, `M_(1) = pi(R^(2)) rho = (1)/(4)M`
Mass of remaining disc, `M_(2) = M - M_(1)`
`= M - (1)/(4)M = (3)/(4)M`
Let centre of mass of remaining disc be at `C_(2)` where `OC_(2) = x`
As `M_(1) xx OC_(1) = M_(2) xx OC_(2)`
`:. (M)/(4) xx R = (3M)/(4)x`
`x = (R )/(3) = alpha R :. alpha = (1)/(3)`