# That's A Weird Frame

A conducting frame is composed by joining the curves $$f(x) = x^{3}$$ and the line $$y = 0$$.

The conducting frame has 0 resistance. A uniform magnetic field of magnitude $$B$$ Tesla is directed inwards as shown. A magical conducting rod parallel to $$y$$-axis starts moving from the origin along the positive direction of $$x$$-axis with intial velocity $$u\text{ m/s}^{-1}$$.

This magical rod has special properties as follows:

1) It has a finite mass $$m \text{ kg}$$ .

2) Its resistance per unit length $$\sigma$$ varies as $$\sigma = \sigma_{0}(1+x^{4}) \dfrac{\Omega}{m}$$ where $$x$$ is the distance of the rod from the origin.

If the distance travelled by the rod till it comes to rest is $$L$$
Find $$\left \lfloor L \right \rfloor$$

Details:

Take $$m =1 \text{ kg}, B = 1\text{ T}, u = 2\text{ m/s}^{-1} ,\sigma_{0} = 1 \dfrac{\Omega}{m}$$.

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