A circular disc of radius $R$ is removed from a bigger circular disc of radius $2R$, such that the circumference of the discs coincide. The centre of mass of the new disc is $\frac{\alpha}{R}$ from the centre of the bigger disc. The value of $\alpha$ is :

Question

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