Question

A vessel at rest explodes breaking it into three pieces. Two pieces having equal mass fly off perpendicular to one another with the same speed of 30 m/s. The third piece has three times the mass of each of the other two pieces. What is the direction (w.r.t. the pieces having equal masses) and magnitude of its velocity immediately after the explosion?

• A. $10\sqrt{2},{135}^o$
• B. $10\sqrt{2},{90}^o$
• C. $10\sqrt{2},{60}^o$
• D. $10\sqrt{2},{30}^o$

Answer 1

The correct option is A $10\sqrt{2},{135}^o$

Initially the vessel having mass $m$ is at rest.

According to the question, $x+x+0.3x=m$ $⟹x=0.2m$

Thus the masses of the three fragments be $0.2m,0.2m$ and $0.6m$

Let the third fragment fly off with velocity $v$ making an angle $\varphi$.

Conservation of momentum in y-direction :

$0.6m\left(vsin\theta \right)=0.2m\left(30\right)$ .........(1)

Conservation of momentum in x-direction :

$0.6m\left(vcos\theta \right)=0.2m\left(30\right)$ .........(2)

Dividing (1) and (2) we get, $tan\theta =1$ $⟹\theta ={45}^o$

$\therefore$ $\varphi ={180}^o-{45}^o={135}^o$

Squaring and adding (1) and (2) we get, $\left(0.6mv{)}^2\right(si{n}^2\theta +co{s}^2\theta )=[0.2m\left(30\right)+0.2m\left(30\right){]}^2$

$\therefore$ $0.6mv=0.2m\left(30\right)\times \sqrt{2}$

$⟹v=10\sqrt{2}$ $m/s$