Carpet Rolling 101

A carpet is rolled into the form of a cylinder (by rolling it along the length) of radius 27140 m\frac{27}{140}\text{ m} and it is kept on a rough horizontal floor. The carpet is given a negligible (gentle) push and it starts to unroll without slipping. Calculate the horizontal velocity in m/s\text{m}/\text{s} of the axis of the cylindrical part of the carpet when its radius becomes 27280\frac{27}{280}.

Note: Approximate gg to be 10 m/s2.10 \text{ m}/\text{s}^2.

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