Comprehension Type Two smooth balls \( \mathrm{A} \) and \( \mathrm{B} \), each of mass \( m \) ....

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Comprehension Type
Two smooth balls \( \mathrm{A} \) and \( \mathrm{B} \), each of mass \( m \) and radius \( \mathrm{R} \), have their centres 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.
Coefficient of restitution during the collision is changed to \( \frac{1}{2} \), keeping all others parameters unchanged. What is the velocity of the ball B after the collision?
(1) \( \frac{1}{2}(3 \sqrt{3} i+9 j) \mathrm{m} / \mathrm{s} \)
(2) \( \frac{1}{4}(9 i-3 \sqrt{3} j) \mathrm{m} / \mathrm{s} \)
(3) \( (6 i+3 \sqrt{3} j) \mathrm{m} / \mathrm{s} \)
(4) \( (6 i-3 \sqrt{3} j) \mathrm{m} / \mathrm{s} \)
\( \mathrm{P} \)
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