Question

Newton's Third law is equivalent to the:

• A. law of conservation of linear momentum
• B. law of conservation of angular momentum
• C. law of conservation of energy
• D. law of conservation of energy and mass

Answer 1

Answer: (A)

law of conservation of linear momentum

Let us consider an isolated system of two bodies A & B mutually interacting with each other ,provided there is no external force acting on the system.

Let $F_{AB}$ force exerted on body B by body A. Similarly ,let $F_{BA}$ be the force exerted by body B on A .Suppose that due to these forces $F_{AB}$ & $F_{BA}$, $\frac{d{p}_1}{dt}$ and $\frac{d{p}_2}{dt}$ be the rate of the change of momentum of these bodies respectively.

Then, $F_{AB}=\frac{d{p}_A}{dt}$

and $F_{BA}=\frac{d{p}_B}{dt}$

Adding above two

$F_{AB}+F_{BA}=\frac{d{p}_A}{dt}+\frac{d{p}_B}{dt}=\frac{d(p_A+p_B)}{dt}$

When no external force acts on the system, then

$\frac{d(p_A+p_B)}{dt}=0$

$F_{AB}+F_{BA}=0$

$F_{AB}=-F_{BA}$