# A particle of mass ' m ' is moving with speed ' 2 v '

Question:

A particle of mass ' $m$ ' is moving with speed ' $2 v$ ' and collides with a mass ' $2 m$ ' moving with speed ' $v$ ' in the same direction. After collision, the first mass is stopped completely while the second one splits into two particles each of mass ' $m$ ', which move at angle $45^{\circ}$ with respect to the original direction.

The speed of each of the moving particle will be:

1. (1) $\sqrt{2} v$

2. (2) $2 \sqrt{2} v$

3. (3) $v /(2 \sqrt{2})$

4. (4) $v / \sqrt{2}$

Correct Option: , 2

Solution:

(2) $m(2 v)+2 m v=0+2 m v^{\prime} \cos 45^{\circ}$

or $v^{\prime}=2 \sqrt{2} v$