A bead of mass \( m \) and diameter \( d \) is sliding back and for...

A bead of mass \( m \) and diameter \( d \) is sliding back and forth with speed \( \mathrm{v} \) on a wire of length
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\( \mathrm{L} \) held between two rigid. Walls assume that the collisions with the wall are perfectly elastic and there is no friction. The average force that the bouncing bead exerts on one of the walls is
(1) \( \frac{m v^{2}}{L-d} \)
(2) \( \frac{m v^{2}}{L+d} \)
(3) \( \frac{2 m v^{2}}{L-d} \)
(4) \( \frac{2 m v^{2}}{L+d} \)