Question

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

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

Answer 1

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

Let the third fragment moved with a velocity $v^{\prime }$ at an angle $\theta$ along with the x axis.
Before explosion, initial momentum $=0$
Apply conservation momentum in x-direction:
$0=mv+m{v}^{\prime }cos\theta$ - (1)
Similarly in y- direction:
$0=mv+m{v}^{\prime }sin\theta$ - (2)
By solving (1) and (2) we get,
$\theta ={45}^0$
Then, from equation (1)
$v^{\prime }=\frac{v}{cos\theta }=\frac{v}{cos45}=v\sqrt{2}$