# Slippery Pulley!

A heavy, long, inelastic chain of length $$L$$ is placed almost symmetrically onto a light pulley which can rotate about a fixed axle, as shown in the figure. If :

I) It's velocity when it leaves the pulley can be represented by $$v_{break} = \dfrac{L^wg^x}{y}$$

II) And height $$h$$ climbed by the end which is going up before losing contact of the pulley can be represented as $$h_{break} = \dfrac{L}{z}$$

Evaluate $$\large \dfrac{w+x}{2} + y + z +1$$

Assumumptions

• Take the pulley to be massless and thus performing pure rolling.
• The chain goes up due to slight asymmetry.
• $$w,~x,~y$$ and $$z$$ are numerical constants $$\in \mathbb{N}$$ and can have any value!
• Take radius $$R$$ of the pulley to be very small, i.e. $$R\ll L$$
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