Two smooth balls A and B, each of mass \( m \) and radius \( \mathrm{R} \), have their centers a....

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Two smooth balls A and B, each of mass \( m \) and radius \( \mathrm{R} \), have their centers at \( (0,0, R) \) and at \( (5 R,-R, R) \) respectively, in a coordinate system as shown. Ball \( A \), moving along positive \( x \)-axis, collides with ball \( B \). Just before the collision, speed of ball \( A \) is \( 4 \mathrm{~m} / \mathrm{s} \) and ball \( B \) is stationary. The collision between the balls is elastic.

Velocity of the ball A just after the collision is
(1) \( (i+\sqrt{3} j) \mathrm{m} / \mathrm{s} \)
(2) \( (i-\sqrt{3} j) \mathrm{m} / \mathrm{s} \)
(3) \( (2 i+\sqrt{3} j) \mathrm{m} / \mathrm{s} \)
(4) \( (2 i+2 j) \mathrm{m} / \mathrm{s} \)


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