Question

The spacecraft of mass $M$ moves with velocity $V$ in free space at first, then it explodes breaking into two pieces. If after explosion a piece of mass $m$ comes to rest, the other piece of spacecraft will have a velocity:

• A. $\frac{MV}{(M-m)}$
  
• B. $\frac{MV}{(M+m)}$
  
• C. $\frac{mV}{\left(Mm\right)}$
  
• D. $\frac{mV}{(M+m)}$
  

Answer 1

The correct option is A $\frac{MV}{(M-m)}$

Initial momentum of the system $P_i=MV$

Let the mass of one part be $m$

Its velocity $V=0$

So, mass of other part $m^{\prime }=M-m$

Let its velocity be $V^{\prime }$.

Final momentum of the system $P_f=mV+m^{\prime }{V}^{\prime }$

Or $P_f=0+(M-m)V^{\prime }=(M-m)V^{\prime }$

Applying the conservation of linear momentum $P_f=P_i$

$\therefore (M-m)V^{\prime }=MV$

$⟹V^{\prime }=\frac{MV}{M-m}$