Solution
Correct Option: (b)
To understand this, we apply the Work-Energy Theorem, which states that the work done by the net force on an object results in a change in its kinetic energy:
$$ W_{net} = \Delta K = K_f – K_i $$Consider the bullet inside the barrel. The expanding gases exert a large force $F$ on the bullet as it travels down the length of the barrel.
If we assume the average force exerted by the gas is $F_{avg}$ and the length of the barrel is $L$, the work done on the bullet is:
$$ W = F_{avg} \cdot L $$Since the bullet starts from rest ($K_i = 0$), the final kinetic energy is equal to the work done:
$$ K_f = F_{avg} \cdot L $$From this relation, it is clear that for a longer barrel length $L$, the work done by the expanding gases is greater. Consequently, the bullet acquires a higher kinetic energy (and thus a higher muzzle velocity), which is essential for increasing the range of the gun.
Therefore, the longer barrel allows the force of the expanding gases to act for a longer distance, maximizing the work done.