Question

A mass $3$m, initially at rest at the origin explodes into three fragments of equal mass. Two of the fragments have speed $v$ each and move perpendicular to each other. The third fragment will move with a speed :

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

Answer 1

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

From law of conservation of momentum,
$mv-m{v}^{\prime }\cos \theta =0$ .........(i)
$mv-m{v}^{\prime }\sin \theta =0$ .........(ii)
From Eqs. (i) and (ii), we get
$\theta ={45}^o$
$v^{\prime }=\frac{v}{\cos \theta }=v\sqrt{2}$.