A circular disc of radius \( R \) is removed from a bigger circular disc of radius \( 2 R \) suc...

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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 centre of mass of the new disc is \( \alpha R \) from the centre of the bigger disc. The value of \( \alpha \) is
[AIEEE 2007]
(a) \( 1 / 3 \)
(b) \( 1 / 2 \)
(c) \( 1 / 6 \)
(d) \( 1 / 4 \)
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