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

Answer

`(3)`

Explanation

`vec p _(i) = m_(2) v hat i + m_(1) xx 0`
`vec p_(f) = m_(2) v/2 hat j + m_(1) xx vec v_(1), (v_(1)` = final velocity of A
`vec p_(i) = vec p_(f) Rightarrow m_(2) v hat i = m_(2) v/2 hat j + m_(1) xx vec v_(1)`
`vec v_(1) = (m_(2))/(m_(1)) v hat i - (m_(2))/(m_(1)) v/2 hat j`
`Rightarrow tan theta = (-1/2) Rightarrow theta = tan ^(-1)(-1/2)` to the x-axis.