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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 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
A
$\theta = \tan^{-1}\left(-\frac{1}{2}\right)$ to the x-axis
B
same as that of B
C
opposite to that of B
D
$\theta = \tan^{-1}\left(\frac{1}{2}\right)$ to the x-axis
Detailed Solution
Let A move with speed $v_1$ at angle $\theta$ to the x-axis after the collision.
Momentum along x: $m_1v_1\cos\theta = m_2v$ ...(i)
Momentum along y: $m_1v_1\sin\theta = m_2\frac{v}{2}$ ...(ii) (equal and opposite to B's y-momentum)
Dividing (ii) by (i): $\tan\theta = \frac{1}{2}$
$\theta = \tan^{-1}\left(\frac{1}{2}\right)$ to the x-axis
Momentum along x: $m_1v_1\cos\theta = m_2v$ ...(i)
Momentum along y: $m_1v_1\sin\theta = m_2\frac{v}{2}$ ...(ii) (equal and opposite to B's y-momentum)
Dividing (ii) by (i): $\tan\theta = \frac{1}{2}$
$\theta = \tan^{-1}\left(\frac{1}{2}\right)$ to the x-axis