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 `v//2` in a direction perpendicular to the original direction. The mass A moves after collision in the direction

Options

A. same as that of B
B. opposite to that of B
C. `theta = tan^(-1)(1/2)` to the x-axis
D. `theta = tan^(-1)(-1/2)` to the x-axis

Answer

D

Explanation

According to law of conservation of linear momentum along x - axis, we get
`m_1 xx 0 + m_1 xx v = m_1 v. cos theta , " or " cos theta = (m_2v)/(m_1 v.) " " …(i)`
According to law of conservation of linear momentum along y-axis , we get
`m_1 xx 0 + m_2 xx 0 = m_1 v. sin theta + m_2 (v)/2 , sin theta = -(m_2 v)/(2 m_1 v.) " " ...(ii)`
Divide (ii) by (i), we get
`tan theta = -1/2 " or " theta = tan^(-1)(-1/2) ` to the x-axis .