Two sphere `A and B` of masses `m_(1) and m_(2)` respectivelly colides. A is at rest initally 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 x-axis`
D. `theta = tan^(-1)(-1/2) to the x-axis`

Answer

`(4)`

Explanation

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