# Doubt in Law of mutual interaction

## Main Question or Discussion Point

Book: Classical mechanics (textbook) by Douglas Gregory (cambridge publications)
Law of mutual interaction states that when two particle (let it be P1 and P2) interacts, the particle (P1) induces an instantaneous acceleration (a21) on particle P2 and the particle P2 induces an instantaneous acceleration (a12) on particle (P1). If the (inertial)masses of the particles are same, then the magnitude of acceleration be the same, and the ratios of acceleration will be constant ( for this case it is 1)(consistency relation)
That is what Newton's third law says
My question is for different (inertial)masses the ratio will be constant ( but not unity) ( it does not satisfy consistency relation) Am i right? If yes
My question is consistency relation is important in classical mechanics?

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UltrafastPED
Gold Member
If P1 interacts with P2 then Newton's 3rd law of motion implies that P2 interacts with P1 with an "equal but opposite " force. Then if the masses are M1 and M2 we will have M1*a1 = - M2*a2, and the ratio of the accelerations can be seen to depend upon the masses.

I don't see what your concern is.

It is a core topic in classical mechanics sir.

UltrafastPED
Gold Member
Let me restate: I don't understand what the question is - the algebra seems clear.

I don't see any problems with "consistency" - classical mechanics is self-consistent.

Nugatory
Mentor
My question is for different (inertial)masses the ratio will be constant ( but not unity) ( it does not satisfy consistency relation) Am i right? If yes
The ratio of the accelerations will be constant but not unity for different masses (and it will be the ratio of the masses, themselves constant so it's not surprising that the ratio of the accelerations is constant). This does not violate any consistency condition.

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