Newton's Third Law and Momentum Conservation

Steps:

• System starts at rest, so total momentum is zero and remains zero after firing.
• Bullet gains forward momentum; gun recoils with equal backward momentum to conserve total momentum.
• During firing, gun pushes bullet forward; bullet pushes gun backward with equal force magnitude but opposite direction.
• Kinetic energy of bullet is (1/2)mv²; gun's is (1/2)MV² where M >> m and V = (mv)/M, so gun's KE is much smaller.

Why D is correct:

• Kinetic energy is not equally distributed; it depends on mass and velocity squared, with lighter bullet gaining more KE per momentum unit (KE = p²/(2m)).

Why the others are wrong:

• A: Newton's third law requires action-reaction forces to have equal magnitude.
• B: Newton's third law requires action-reaction forces to be in opposite directions.
• C: Conservation of momentum requires bullet and gun momenta to have equal magnitude (total zero).

Final answer: D