Question

A shell initially at rest explodes into two pieces of equal mass, the two pieces will
A. move with different velocities in different directions
B. move with the same velocity in opposite directions
C. move with the same velocity in the same direction
D. be at rest

Answer 1

Hint:In order to solve this question, we will apply the law of conservation of momentum and then using this principle and equations we will determine the nature of two pieces of shells after the explosion.

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 defined as the product of mass of the body and the velocity of the body.

Complete step by step solution:
According to the question, we have given that a shell was at rest initially and let us assume the mass of the shell was M and its velocity before the explosion is zero $(u = 0)$. So, initial momentum of the system is
${P_i} = Mu \\
\Rightarrow {P_i} = 0 \to (i) \\ $
Now, as said after the explosion shell divides into two pieces of equal mass such that two pieces are denoted as ${m_1} = {m_2} = \dfrac{M}{2}$ and let their velocities be ${v_1},{v_2}$ so the momentum of system after the explosion will be
${P_f} = {m_1}{v_1} + {m_2}{v_2} \\
\Rightarrow {P_f} = \dfrac{M}{2}({v_1} + {v_2}) \to (ii) \\ $
From the principle of conservation of linear momentum we have ${P_i} = {P_f}$ so using equations (i) and (ii) we get,
$0 = \dfrac{M}{2}({v_1} + {v_2}) \\
\therefore {v_1} = - {v_2} \\ $
So, the velocities of both the parts will be equal in magnitude but a negative sign shows that their direction will be exactly opposite to each other.

Hence, the correct answer is option B.

Note: It should be remembered that, other than conservation of linear momentum the other two most important conservation laws are law of conservation of energy where energy remains conserved of the system and conservation of angular momentum in rotational dynamics.