A classical mechanics problem by aditya shah

Classical Mechanics Level 5

Two identical solid cylinders of mass \(m\) and radius \(r\) lie on a smooth horizontal table with a massless string around it.There is enough friction between string and cylinder such that it does not slip on cylinders. The other end of the string is tied to a particle of mass \(m\). If one end of string is pulled with force \(f\) then find the acceleration of particle attached to it.

if the acceleration of particle can be expressed as \(\dfrac{af}{bm}\), where \(a\) and \(b\) are coprime positive integers, find \(a+b\)

Details and Assumptions:

Choose right side to be positive and left side to be negative.


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