Question

The object at rest suddenly explodes into three parts with the mass ratio 2:1:1. The parts of equal masses move at right angles to each other with equal speed $v$. The speed of the third part after the explosion will be:

• A. $2v$
• B. $v/\sqrt{2}$
• C. $v/2$
• D. $\sqrt{2}v$

Answer 1

The correct option is B $v/\sqrt{2}$

Using conservation of linear momentum:
$0=\frac{m}{4}v\hat{j}+\frac{m}{4}v\hat{i}+\frac{m}{2}(v_x\hat{i}+v_y\hat{j})$
$\Rightarrow v_x=\frac{-v}{2}\hat{i}$
$v_y=\frac{-v}{2}\hat{j}$
So, speed $=\frac{v}{\sqrt{2}}$