# Minimum Length of Cart + Pure Rolling!

A uniform disc of mass $$m = 12 \text{ kg}$$ slides down along smooth, friction less hill, which ends in a horizontal plane without break. The disc is released from rest at a height of $$h = 1.25 \text{ m}$$ (it has no initial speed and it does not rotate), and lands on the top of a cart of mass $$M = 6 \text{ kg}$$, which can move on a friction less surface. The coefficient of kinetic friction between the cart and the disc is $$\eta_k = 0.4$$. Find minimum length of the cart (in $$\text{ m}$$) so that the disc begins to roll without slipping before loosing contact with the cart.

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