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

Answer 1

Hint: To answer this question, we will use the rule of conservation of linear momentum, and then we will use this concept and equations to calculate the velocity of the other section of the spacecraft..

Formula used: The principle of conservation of linear momentum says that Initial momentum of a system is always equal to final momentum of a system.
${P_i} = {P_f}$
where $P = mv$ denotes the momentum of a body.

Complete step by step solution:
According to the question, we have given that initial velocity and mass of the space-craft is V and M so, initial momentum of the system is ${P_i} = MV$ and after the explosion it breaks into two pieces and one of the piece having mass m is at rest which means it have zero velocity therefore zero momentum.

 Let $v$ be the velocity of another piece which will have a mass of $M-m$. So the total final momentum of the system is,
${P_f} = (M - m)v$
Now, equate ${P_i} = {P_f}$
using law of conservation of momentum so we get,
$MV = (M - m)v + m \times 0 \\
\therefore v= \dfrac{{MV}}{{(M - m)}} $

Hence, the correct answer is option A.

Note: It should be remembered that, there are two basic laws of conservation other than of linear momentum are law of conservation of energy where energy remains conserved and another is law of conservation of angular momentum in rotational dynamics.