A circular disc of radius $'R'$ is removed from a bigger circular disc of radius $'2R'$ such that the circumference of the disc touch. The center of mass of the new disc is at a distance $'\alpha R'$ from the center of the bigger disc. The value of $\alpha'$ is

Question

$$\begin {array} {1 1} (a)\;\frac{1}{2} & \quad (b)\;\frac{1}{3} \\ (c)\;\frac{1}{4} & \quad (d)\;\frac{1}{6} \end {array}$$