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I know the mathematics F=m(center of mass)*a but I want a mechanical answer.

Please help me analyze the mechanics of it.

I think analyzing the following thought experiment will be of some help though i don't

know how to proceed with it.

Consider two spherical bobs attached to two ends of an elastic string.(rigid rod as a limiting case of elasticity)

When an exact perpendicular force is applied at one bob the bob will accelerate and move along a straight line while the other bob remains at rest. Now due to an increase in length

of the string a tension will be developed and will pull both the bobs toward its center of mass.

I don't know how to proceed with it and can't see why the rotation is about center of mass.