Round and Round

A ball that weights 5N is connected to an elastic rope. Originally the rope is of length 13 cm. when the ball is added. the rope rests in equilibrium at length 14.8 cm. The ball is now made to spin in a vertical circular path. When the ball is turned a 180 degrees through the circle. The length of the rope is again 13 cm. As the ball continues rotating a full 360 degrees and return to its original starting point, if the length of the rope at that point in metres is \(\frac { a }{ b } \) where a and b are co prime then what is the value of \(a+ b\) ?

Take g as 9.81

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