Question

10. Show that Newton's third law of motion is contained in the second law.​

Answer 1

Consider an isolated system of two bodies A & B. Suppose the two bodies interact mutually with one another. Let fBA be the force (action) exerted by A on B. Let dpB/dt be the resulting change of momentum of B. Let fAB be the force (reaction) exerted by B on A.Let dpA/dt be the resulting change of momentum of A. According to Newton's second law,

fBA=dpB/dt & fAB=dpA/dt

Therefore, fBA+fAB=dpB/dt + dpA/dt = d/dt (pB+pA)

In the absence of external force, the rate of change of momentum must be zero i.e., d/dt (pB+pA) must be zero.

Therefore, fBA+fAB =0

or,fBA= -fAB

or, Action= -Reaction

This is nothing but Newton's third law of motion.

Hence, third law of motion is contained in the second law.

Answer 2

${\bold{\huge{\red{\underline{\green{ANSWER}}}}}}$

In the absence of external force,

the rate of change of momentum must be zero

${\bold{\boxed{\pink{ \frac{d}{dt} (pa + pb)}}}}$must be zero.

fPa +fpb=0

fpa=-fpb

This is nothing but Newton's third law of motion. Hence, third law of motion is contained in the second law. Its is the 3rd law of motion.