Two identical balls \( A \) and \( B \), each of mass \( 2 \mathrm{~kg} \) and radius \( R \), a...

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Two identical balls \( A \) and \( B \), each of mass \( 2 \mathrm{~kg} \) and radius \( R \), are suspended vertically from inextensible strings as shown in figure. The third ball \( C \) of mass \( 1 \mathrm{~kg} \) and radius \( r=(\sqrt{2}-1) R \) falls and hits \( A \) and \( B \) symmetrically with \( 10 \mathrm{~m} / \mathrm{s} \). Speed of both \( A \) and \( B \) just after the collision is \( 3 \mathrm{~m} / \mathrm{s} \). Speed of \( C \) just after collision is
(1) \( 2 \mathrm{~m} / \mathrm{s} \)
(2) \( 2 \sqrt{2} \mathrm{~m} / \mathrm{s} \)
(3) \( 5 \mathrm{~m} / \mathrm{s} \)
(4) \( (\sqrt{2}-1) \mathrm{m} / \mathrm{s} \)
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