Question

A space-craft of mass $M$ moves with a velocity $V$ and suddenly explodes into two pieces. If a part of mass $m$ becomes stationary, then the velocity of another part will be :

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

Answer 1

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

Given:

Mass of the spacecraft = $M$

Velocity of the spacecraft = $V$

Mass of one part = $m$, velocity of this part = $0$

Mass of the other part = $M-m$, velocity of this part = $v=?$

No external force is acting on the spacecraft in the explosion. Therefore, the total linear momentum must be conserved.

$\underset{–}{\text{Applying conservation of momentum:}}$

$\text{Total initial linear momentum of the spacecraft}=\text{Total final momentum of the two parts}$

$\Rightarrow MV=m\times 0+(M-m)v$

$\Rightarrow v=\frac{MV}{M-m}$

Hence, option A is correct.