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# Newton’s second law of motion is the real law of motion

Before to know Newton’s second law of motion is the real law of motion we must know all three equations of motion.

Second law of motion  is the real law of motion

The question may be asked as , show that second law of motion is the real law of motion .

***This question is very important for the class 11th examination point of view .

To show it we must prove two things (i) First law contained in the second law and (ii) Third law contained in second law.

(i) ) First law contained in the second law –  As we know according to Newtons second law of motion

Force F = Ma ,

If there is no external force

then F = 0

Or, Ma =0    then we can say    M=0 or a=o , but mass of the body can’t be zero.

Therefore only possible thing is that only acceleration is zero .

But , we know acceleration a= v-u/t ( where , v- final velocity and  u- initial velocity) .

So we can write , v-u/t = 0  i.e v-u=0 or v=u

Since V (final velocity) = u ( initial velocity).

So we can say if body initially is in rest will be in rest and if it is moving with some velocity it will remain in the motion with the same velocity( which is the statement of first law ) . So we can say first law contained in the second law .

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(ii) Third law contained in the second law –  suppose an isolated system of two objects A and B , they interact mutually with one another . Then obviously they will apply force on each other .

Let,  FAB – Force on A due to B ,

And  FBA – Force on B due to A .

Let dpa and dpb is the change in momentum in A and B respectively in small time dt .

Then from Newton’s second law –

FAB = dpA/dt   ………………………(i)

and, FBA= dpB/dt …………………..(ii)

FAB+ FBA= dpB/dt + dpA/dt   ……….(iii)

In the absence of external force , the rate in change in momentum of the system will be zero .

i.e. dpB/dt + dpA/dt  = 0

Therefore , FAB+ FBA=0 ;

Or, FAB= -FBA ( which is third law )

So we can say Newtons third law contained in the second law .

Therefore we can say Newton’s second law of of motion is the real law of motion.

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