The racket in the diagram has mass M and is free to rotate about a fixed smooth axis A which is paralel to the plane of the racket and perpendicular to its handle.

The racket in the diagram has mass M and is free to rotate about a fixed smooth axis A which is paralel to the plane of the racket and perpendicular to its handle. The moment of inertia of the racket about a parallel axis through its centre of mass, G, is Mk2 . When the racket is at rest, it is hit at the point P with an impulse J1 perpendicular to its plane and to the axis of rotation. AG = h and AP =  d.
i) Find the value of d which ensures that the impulsive reaction, J2 at A is zero.
ii) Show that this value of d is equal to the length of a simple pendulum which would perform small oscillations about the axis through A with the same period as the racket.

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