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Two spheres $A$ and $B$ of masses $m_{1}$ and $m_{2}$ respectively collide. $A$ is at rest initially and $B$ is moving with velocity $2 v$ along x-axis. After collision $B$ has a velocity $v$ in a direction perpendicular to the original direction. The mass $A$ moves after collision in the direction.

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$θ = \tan^{- 1} (\frac{1}{2})$ to the x-axis

$θ = \tan^{- 1} (- \frac{1}{2})$ to the x-axis

same as that of $B$

opposite to that of $B$

answer is A.

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Detailed Solution

Case-I

$p_{x} = m_{2} 2 v p_{y} = m_{2} v ∴ \tan θ = \frac{p_{y}}{p_{x}} = - \frac{1}{2}$

Case-II

similarly

$p_{x} = m_{2} v p_{y} = - m_{2} v ∴ \tan θ = \frac{p_{y}}{p_{x}} = \frac{1}{2}$

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