Question

An object initially at rest explodes, disintegrating into $3$ parts of equal mass. Parts $1$ and $2$ have the same initial speed $v$, the velocity vectors being perpendicular to each other. Part $3$ will have an initial speed of :

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

Answer 1

The correct option is A $\sqrt{2}v$

Total linear momentum must be conserved.

Initial momentum $=$ final momentum

$0=\frac{m}{3}v\hat{j}+\frac{m}{3}v\hat{i}+\frac{m}{3}(v_x\hat{i}+v_y\hat{j})$

$\Rightarrow v_x=-v\hat{j}$

$v_y=-v\hat{j}$

Speed $=v\sqrt{2}$