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# what is reduced mass?plz...explain with an example,where  it is used  and what are the conditions? Badiuddin askIITians.ismu Expert
147 Points
11 years ago

Dear neru

The reduced mass m (kg) of a system of two bodies is determined as

1/μ  = 1/ma   + 1/mb

where ma and mb are the masses (kg) of the bodies.

Suppose you have 2 objects with masses M and m that exert a force on each other as shown.

So  mass, force & acceleration

 Quantity Mass M mass m Mass M m Force -F F Acceleration aM = -F/M am = F/m

Newton's laws of action/reaction have been used.  Calculating quantities such as distances between them looks complex, but there is a nifty tool.  View the system in the reference frame of one of the objects (say mass M).

Now mass M is stationary, but mass m is still free to move under the force F, with one catch.  When one views a situation in the frame of an object with acceleration a, all objects have as there acceleration the acceleration due to the forces on it minus this acceleration a.  For the case of mass m

am´ = F/m - aM = F·(1/m + 1/M) = F/(m·M/(m + M))

In other words, mass m behaves as if it instead has a mass μ = m·M/(m + M).  This is called the reduced mass.

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