Two smooth balls A and B each of mass m and radius R, have their centers at (0, 0, R) and at $(5R, - R, R)$ 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 $4 m/s$ and ball B is stationary. The collision between the balls is elastic. Velocity of the ball A just after the collision is

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(\hat{i} - \sqrt{3} \hat{j}) m / s

(2 \hat{i} + \sqrt{3} \hat{j}) m / s

(2 \hat{i} + 2 \hat{j}) m / s

(\hat{i} + \sqrt{3} \hat{j}) m / s

answer is A.

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Detailed Solution

$\sin θ = \frac{R}{2R} = \frac{1}{2}$

$θ = 30 °$

$v_{1} = 4 \sin 30$

$v_{1} = 2 m/s$

Question Image

$v_{A} = v_{1} \cos 60 i + v_{1} \sin 60 j$

$= 2 \times \frac{1}{2} i + \frac{\sqrt{3}}{2} j = i + \sqrt{3} j$

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