A thin uniform square plate with side \( I \) and mass \( M \) can rotate freely about a station...

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A thin uniform square plate with side \( I \) and mass \( M \) can rotate freely about a stationary vertical axis coinciding with one of its sides. A small ball of mass \( m \) flying with velocity \( \mathbf{v} \) at right angles to the plate strikes elastically the centre of it. Find :
the horizontal component of the resultant force which the axis will exert on the plate after the impact.
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