When a bullet is fired from a gun, what happens to the gun itself according to the law of conservation of momentum?

Introduction / Context:
This question illustrates the law of conservation of linear momentum using the familiar example of firing a bullet from a gun. Before firing, both gun and bullet are at rest, so the total momentum of the system is zero. After firing, the bullet moves forward with high speed, and the gun responds in a characteristic way. Understanding this behaviour is essential in mechanics because it connects force, mass, and motion and explains why firearms produce a backward kick or recoil when used.

Given Data / Assumptions:

• The system consists of a gun and a bullet.
• Initially, both gun and bullet are at rest, so total momentum is zero.
• On firing, the bullet is projected forward with a certain velocity.
• No external horizontal forces act on the system during the short firing interval.

Concept / Approach:
The law of conservation of linear momentum states that if no external force acts on a system, the total momentum of the system remains constant. In the horizontal direction for a gun bullet system, external forces such as friction can be neglected during the brief firing event. Therefore, the momentum gained by the bullet must be balanced by an equal and opposite momentum of the gun. Because the gun has a much larger mass than the bullet, it moves backward with a smaller velocity, but the product of mass and velocity (momentum) has equal magnitude and opposite direction to the bullet's momentum.

Step-by-Step Solution:
Step 1: Initially, gun and bullet are at rest, so total momentum is zero.Step 2: When the gun is fired, the bullet of mass m_b moves forward with velocity v_b, so its momentum is m_b * v_b.Step 3: To conserve momentum, the gun of mass m_g must acquire momentum of equal magnitude but opposite direction.Step 4: Let the gun recoil velocity be v_g backward; then m_g * v_g = m_b * v_b in magnitude.Step 5: The gun therefore recoils backward with momentum equal in magnitude but opposite in direction to that of the bullet, satisfying momentum conservation.

Verification / Alternative check:
Observations from real life confirm this analysis. When a shotgun or rifle is fired, the shooter feels a backward kick. Heavier guns have smaller recoil velocities, while lighter guns or higher powered cartridges produce stronger recoil effects. This matches the relationship m_g * v_g = m_b * v_b. In addition, recoil damping systems and shoulder supports are used to manage this backward motion. If the gun did not move, total momentum after firing would not be zero, contradicting the conservation law. Therefore, a backward recoil is both theoretically and practically necessary.

Why Other Options Are Wrong:
Option A, stating that the gun moves slightly forward, contradicts the requirement that momentum must be opposite to that of the bullet. Option B, saying the gun jumps only upward, might describe some observed motion due to the shooter's grip and gravity, but the primary reaction is backward, not purely upward. Option C, claiming that the gun does not move, violates conservation of momentum because the bullet acquires forward momentum that must be balanced. Only option D correctly states that the gun recoils backward with the same magnitude of momentum as the bullet but in the opposite direction.

Common Pitfalls:
Some learners think of the gun as fixed and assume that only the bullet moves, ignoring the fact that the gun is free to recoil. Another pitfall is to confuse velocity with momentum and forget that a large mass with small velocity can have the same momentum as a small mass with large velocity. Remember to apply conservation laws to the entire system and not only to one part. Doing so will guide you to recognise recoil as an unavoidable consequence of momentum conservation in firearms and similar systems like rockets and jet propulsion.

Final Answer:
The gun recoils backward with the same momentum as the bullet in the opposite direction