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

Explanation

To solve the problem, we will use the principle of conservation of momentum. The problem involves two spheres, A and B, with given masses and velocities before and after the collision. Let's break down the solution step by step.

### Step 1: Define the Given Information
- Mass of sphere A: \( m_1 \)
- Mass of sphere B: \( m_2 \)
- Initial velocity of sphere A: \( u_1 = 0 \) (at rest)
- Initial velocity of sphere B: \( u_2 = v \) (moving along the x-axis)
- Final velocity of sphere B after collision: \( v_2' = \frac{v}{2} \) (perpendicular to the original direction, which we can assume is in the positive y-direction)
...