Question

Conservation of momentum is a direct consequence of which law?

• A. Newton's first law of motion
• B. Newton's second law of motion
• C. Newton's third law of motion
• D. Newton's law of gravitation

Answer 1

The correct option is C Newton's third law of motion

Conservation of momentum is a direct consequence of Newton's third law.

Consider a collision between two objects A and B. At the time of their collision, object A applies a force $F_{BA}$ on object B. According to Newton's third law, an equal and opposite force $F_{AB}$ is acted on object A by object B.

Therefore,
$F_{BA}=-F_{AB}$.

Also, during the collision, they touch each other for the same duration t.

Hence,
$F_{BA}\times t=-F_{AB}\times t$
According to the Second law of motion,
the product of force and time = change in momentum.
$\Rightarrow m_B\Delta v_B=-m_A\Delta v_A\Rightarrow m_B\Delta v_B+m_A\Delta v_A=0$

This is the mathematical form of the law of conservation of momentum.