Two spheres \(\mathrm{S}_1\) and \(\mathrm{S}_2\) of masses \(\mathrm{m}_1\) and \(\mathrm{m}_2\) respectively collide with each other. Initially \(\mathrm{S}_1\) is at rest and \(\mathrm{S}_2\) is movingwith velocity v along x -axis. After collision \(\mathrm{S}_2\) has a velocity \(\frac{\mathrm{v}}{2}\) in a direction perpendicular to the original direction. The sphere \(\mathrm{S}_1\) moves after collision

1. A with a velocity of magnitude \(\frac{\mathrm{m}_2}{\mathrm{~m}_1} \mathrm{v} \frac{\sqrt{5}}{2}\)
2. B with a velocity in the direction \(\theta=\tan ^{-1}\left(-\frac{1}{3}\right)\) to the \(x\)-axis
3. C with a velocity whose direction makes an angle \(\theta\) with \(x\)-axis such that \(\theta=\tan ^{-1}\left(\frac{1}{2}\right)\) or \(\theta=\tan ^{-1}\left(-\frac{1}{2}\right)\)
4. D with a velocity of magnitude \(\frac{m_1}{2 m_2} v \sqrt{5}\)