Silly rods

The figure below shows a non uniform metre stick AB having the linear mass density variation \(\lambda=\lambda_{o}x\) where \(\lambda_{o}\) is a constant and \(x\) is the distance from end \(A\), placed on smooth horizontal surface.

In the first experiment, the rod is pivoted at \(A\) and force \(F\) is applied perpendicular to the rod at the other end \(B\) and in the second experiment, the rod is pivoted at \(B\) and the force is applied perpendicular to the rod at the end \(A\).

If in the first case angular acceleration is \(\alpha_{A}\) and in the second case it is \(\alpha_{B}\) then

Refer to my set

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