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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 v along x-axis. After the collision, B has a velocity $\frac{v}{2}$ in a direction perpendicular to the original direction. The mass A moves after collision in the direction:

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opposite to that of B.

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

same as that of B.

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

answer is D.

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Detailed Solution

Let velocity of A is $v_{1}$ at angle $θ$ with initial direction of motion of B.

$m_{1} v_{1} \cos θ = m_{2} v - - - - - (i)$

$m_{1} v_{1} \sin θ = \frac{m_{2} v}{2} - - - - (ii)$

Divide (ii) by (i), we get:

$\tan θ = \frac{1}{2} \Rightarrow θ = \tan^{- 1} (\frac{1}{2})$

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