The mass of the gun is much greater than the mass of the bullet.
Explanation
The phenomenon of recoil is governed by Newton’s Third Law of Motion, which states that for every action, there is an equal and opposite reaction. Additionally, Newton’s Second Law of Motion ($F = ma$) establishes the relationship between force, mass, and acceleration.
Detailed Analysis:
- Force Equality: When a gun is fired, it exerts a forward force on the bullet. Simultaneously, the bullet exerts an equal and opposite backward force on the gun. Therefore, the magnitude of the force ($F$) acting on both the gun and the bullet is identical.
- Role of Mass: According to Newton’s Second Law, acceleration ($a$) is inversely proportional to mass ($m$) for a given force ($a = \frac{F}{m}$).
- Conclusion: Since the mass of the gun is significantly greater than the mass of the bullet, the acceleration produced in the gun (recoil) is much smaller than the acceleration of the bullet, despite the forces being equal in magnitude.
Analysis of Incorrect Options:
- The force acting on the gun is less than the force on the bullet.: Incorrect. The forces are equal in magnitude according to Newton's Third Law.
- The gun is held by a shooter who absorbs the momentum.: Incorrect. While a shooter absorbs the recoil, the physical reason for the lower acceleration compared to the bullet is the mass difference, not the external holding of the gun.
- The duration of the force on the gun is shorter.: Incorrect. The action and reaction forces exist for the exact same duration.
Key Takeaway:
While action and reaction forces are equal in magnitude, the resulting accelerations differ because acceleration is inversely proportional to the mass of the object ($a \propto \frac{1}{m}$).